Liquid crystal element, deflection element, and eyeglasses

ABSTRACT

A liquid crystal element ( 100 ) refracts and outputs light. The liquid crystal element ( 100 ) includes a first electrode ( 1 ), a second electrode ( 2 ), an insulating layer ( 21 ) that is an electric insulator, a resistance layer ( 22 ), a liquid crystal layer ( 23 ) including liquid crystal, and a third electrode ( 3 ). The insulating layer ( 21 ) is disposed between each location of the first and second electrodes ( 1 ) and ( 2 ) and the resistance layer ( 22 ) to insulate the first and second electrodes ( 1 ) and ( 2 ) from the resistance layer ( 22 ). The resistance layer ( 22 ) has an electrical resistivity higher than that of the first electrode ( 1 ) and lower than that of the insulating layer ( 21 ). The resistance layer ( 22 ) and the liquid crystal layer ( 23 ) are disposed between the insulating layer ( 21 ) and the third electrode ( 3 ). The resistance layer ( 22 ) is disposed between the insulating layer ( 21 ) and the liquid crystal layer ( 23 ). The insulating layer ( 21 ) has a thickness (ts) smaller than a thickness (th) of the resistance layer ( 22 ).

TECHNICAL FIELD

The present invention relates to a liquid crystal element, a deflectionelement, and eyeglasses.

BACKGROUND ART

A liquid crystal cylindrical lens disclosed in Patent Literature 1includes a first electrode, a plurality of second electrodes, aplurality of third electrodes, an insulating layer, a plurality of firsthigh-resistance layers, a plurality of second high-resistance layers,and a liquid crystal layer.

The second electrodes and the third electrodes are arranged adjacent toone another with spaces therebetween. A first voltage is applied to eachof the second electrodes, while a second voltage is applied to each ofthe third electrodes. The first voltage has the same frequency as thesecond voltage. The respective spaces between the second electrodes andthe third electrodes are substantially the same among the spaces betweenthe second electrodes and the third electrodes.

CITATION LIST Patent Literature [Patent Literature 1]

Japanese Patent Application Laid-Open Publication No. 2012-141552

SUMMARY OF INVENTION Technical Problem

However, spaces each between electrodes (also referred to below as an“inter-electrode distances”) may differ among electrodes in a singleliquid crystal lens depending on a type of the liquid crystal lens (alsoreferred to below as a “first case”). Alternatively, in a configurationin which inter-electrode distances are the same among electrodes in asingle liquid crystal lens or a single liquid crystal lens includes onlyone pair of electrodes, the inter-electrode distances may differ amongliquid crystal lenses having different specifications (also referred tobelow as a “second case”).

Meanwhile, favorable frequencies of voltages to be applied to therespective electrodes and favorable electrical resistivities of thehigh-resistance layers vary depending on the inter-electrode distances.

In the first case, therefore, it is accordingly necessary in some casesto determine a plurality of favorable frequencies corresponding to therespective inter-electrode distances for the single liquid crystal lens.Furthermore, it is necessary in some cases to determine a plurality offavorable electrical resistivities corresponding to the respectiveinter-electrode distances and provide a plurality of high-resistancelayers having the respective favorable electrical resistivities for thesingle liquid crystal lens. This complicates design of the liquidcrystal lens and increases manufacturing cost of the liquid crystallens.

Alternatively, in the second case, it is necessary in some cases todetermine favorable frequencies corresponding to the inter-electrodedistances for the respective liquid crystal lenses different inspecification. Moreover, it is necessary in some case to determinefavorable electrical resistivities corresponding to the respectiveinter-electrode distances and provide high-resistance layers having therespective favorable electrical resistivities for the respective liquidcrystal lenses different in specification. This complicates design ofthe liquid crystal lenses and increases manufacturing cost of the liquidcrystal lenses as compared to a case where the favorable frequencies areequal and the favorable electrical resistivities are equal among liquidcrystal lenses different in specification.

The present invention has been made in view of the foregoing and has itsobject of providing a liquid crystal element, a deflection element, andeyeglasses in which variation in favorable frequency and favorableelectrical resistivity depending on inter-electrode distances can beprevented.

Another object of the present invention is to provide a liquid crystalelement, a deflection element, and eyeglasses that can form an electricpotential gradient suitable for a Fresnel lens.

Solution to Problem

According to a first aspect of the present invention, a liquid crystalelement refracts and outputs light. The liquid crystal element includesa first electrode, a second electrode, an insulating layer that is anelectric insulator, a resistance layer, a liquid crystal layer includingliquid crystal, and a third electrode. The insulating layer is disposedbetween each location of the first electrode and the second electrodeand the resistance layer, and insulates the first electrode and thesecond electrode from the resistance layer. The resistance layer has anelectrical resistivity that is higher than an electrical resistivity ofthe first electrode and lower than an electrical resistivity of theinsulating layer. The resistance layer and the liquid crystal layer aredisposed between the insulating layer and the third electrode. Theresistance layer is disposed between the insulating layer and the liquidcrystal layer. The insulating layer has a thickness that is smaller thana thickness of the resistance layer.

In the liquid crystal element according to the present invention, thethickness of the insulating layer is preferably equal to or less than ⅕of the thickness of the resistance layer.

In the liquid crystal element according to the present invention, it ispreferable that the first electrode and the second electrode constitutea unit electrode and the unit electrode is provided as a plurality ofunit electrodes. Preferably, one unit electrode of at least two unitelectrodes included in the unit electrodes has a width different from awidth of the other of the at least two unit electrodes and widths of theunit electrodes each indicate a distance between the first electrode andthe second electrode.

A liquid crystal element according to a second aspect of the presentinvention refracts and outputs light. The liquid crystal elementincludes a plurality of unit electrodes each including a first electrodeand a second electrode, a resistance layer, a liquid crystal layerincluding liquid crystal, and a third electrode. The resistance layerhas an electrical resistivity that is higher than an electricalresistivity of the first electrode and lower than an electricalresistivity of an insulator. The liquid crystal layer is disposedbetween the unit electrodes and the third electrode. The resistancelayer is disposed between the liquid crystal layer and the unitelectrodes, or the unit electrodes are disposed between the resistancelayer and the liquid crystal layer. The unit electrodes are opposite tothe resistance layer with no insulator therebetween. Widths of the unitelectrodes are determined such that a ratio of refracted light to lightoutput from the liquid crystal layer is larger than a ratio ofdiffracted light to the light output from the liquid crystal layer. Thewidths of the unit electrodes each indicate a distance between the firstelectrode and the second electrode.

Preferably, the liquid crystal element according to the presentinvention further includes a center electrode having a ring shape.Preferably, the center electrode and the unit electrodes are arrangedconcentrically about the center electrode as a center.

A liquid crystal element according to a third aspect of the presentinvention refracts and outputs light. The liquid crystal elementincludes a core electrode, a center electrode surrounding the coreelectrode, a unit electrode including a first electrode and a secondelectrode and surrounding the center electrode, an insulating layer thatis an electrical insulator, a resistance layer, a liquid crystal layerincluding liquid crystal, and a third electrode. The insulating layer isdisposed between each location of the core electrode and the centerelectrode and the resistance layer to insulate the core electrode andthe center electrode from the resistance layer, and disposed betweeneach location of the first electrode and the second electrode and theresistance layer to insulate the first electrode and the secondelectrode from the resistance layer. The resistance layer has anelectrical resistivity that is higher than an electrical resistivity ofthe core electrode and lower than an electrical resistivity of theinsulating layer. The resistance layer and the liquid crystal layer aredisposed between the insulating layer and the third electrode. Theresistance layer is disposed between the insulating layer and the liquidcrystal layer. A distance from a center of gravity of the core electrodeto an outer edge of the core electrode is larger than a width of thecenter electrode, a width of the first electrode, or a width of thesecond electrode.

In the liquid crystal layer according to the present invention, it ispreferable that the core electrode has a discoid shape and the centerelectrode has a ring shape. The core electrode preferably has a radiusthat is equal to or larger than ⅕ of the radius of the center electrode.

In the liquid crystal element according to the present invention, it ispreferable that a first voltage is applied to the first electrode, asecond voltage is applied to the second electrode, a core voltage isapplied to the core electrode, and a center voltage is applied to thecenter electrode. It is preferable that a frequency of the core voltagediffers from a frequency of the first voltage and a frequency of thesecond voltage and a frequency of the center voltage differs from thefrequency of the first voltage and the frequency of the second voltage.

In the liquid crystal element according to the first to third aspects,the first electrode and the second electrode preferably constitute aunit electrode. In the unit electrode, it is preferable that a distancebetween the first electrode and the second electrode is larger than awidth of the first electrode and larger than a width of the secondelectrode.

A deflection element according to a fourth aspect of the presentinvention deflects and outputs light. The deflection element includestwo liquid crystal elements each according to any of the first to thirdaspects. In one liquid crystal element of the two liquid crystalelements, the first electrode and the second electrode each extend in afirst direction. In the other liquid crystal element of the two liquidcrystal elements, the first electrode and the second electrode eachextend in a second direction perpendicular to the first direction. Theone liquid crystal element and the other liquid crystal element areoverlaid one on the other.

Eyeglasses according to a fifth aspect of the present invention includesa liquid crystal element according to any one of the first to thirdaspects, a controller that controls a first voltage applied to the firstelectrode and a second voltage applied to the second electrode, and apair of temple members. The liquid crystal element refracts and outputsthe light.

Advantageous Effects of Invention

According to the present invention, variation in favorable frequency andthe favorable electrical resistivity depending on the inter-electrodedistances can be reduced. Furthermore, according to the presentinvention, an electric potential gradient suitable for a Fresnel lenscan be formed.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1A is a plan view illustrating a liquid crystal element accordingto Embodiment 1 of the present invention. FIG. 1B is a cross-sectionalview illustrating the liquid crystal element according to Embodiment 1.

FIG. 2A is a cross-sectional view illustrating the liquid crystalelement according to Embodiment 1. FIG. 2B is a diagram illustrating anelectric potential gradient formed in the liquid crystal elementaccording to Embodiment 1. FIG. 2C is a diagram illustrating arefractive index gradient formed in the liquid crystal element accordingto Embodiment 1.

FIG. 3 is a diagram illustrating incident light entering the liquidcrystal element and output light output from the liquid crystal elementaccording to Embodiment 1.

FIG. 4 is a plan view illustrating a liquid crystal element according toEmbodiment 2 of the present invention.

FIG. 5 is a plan view illustrating in an enlarged scale a part of theliquid crystal element according to Embodiment 2.

FIG. 6 is a cross-sectional view illustrating a part of the liquidcrystal element according to Embodiment 2.

FIG. 7 is a cross-sectional view illustrating a part of the liquidcrystal element according to Embodiment 2.

FIG. 8A is a plan view illustrating the liquid crystal element accordingto Embodiment 2. FIG. 8B is a diagram illustrating an electric potentialgradient formed in the liquid crystal element according to Embodiment 2.

FIG. 9 is a cross-sectional view illustrating a part of a liquid crystalelement according to Embodiment 3 of the present invention.

FIG. 10 is a graph representation showing a relationship between unitelectrode ordinal and diameter of unit electrodes of the liquid crystalelement according to each of Embodiment 3 and a comparative example.

FIG. 11 is a cross-sectional view illustrating a part of a liquidcrystal element according to Embodiment 4 of the present invention.

FIG. 12 is an exploded perspective view illustrating a deflectionelement according to Embodiment 5 of the present invention.

FIG. 13 is a diagram illustrating an eyeglass device according toEmbodiment 6 of the present invention.

FIG. 14 is a diagram illustrating an electric potential gradient in aliquid crystal element according to Comparative Example 1.

FIG. 15 is a diagram illustrating electric potential gradients in aliquid crystal element according to Example 1 of the present invention.

FIG. 16 is a diagram illustrating electric potential gradients in aliquid crystal element according to Example 2 of the present invention.

FIG. 17 is a diagram illustrating electric potential gradients in aliquid crystal element according to Example 3 of the present invention.

FIG. 18A is a diagram illustrating electric potential gradients in aliquid crystal element according to Comparative Example 2. FIG. 18B is adiagram illustrating equipotential lines and electric lines of force inthe liquid crystal element according to Comparative Example 2.

FIG. 19A is a diagram illustrating an electric potential gradient in aliquid crystal element according to Example 4 of the present invention.FIG. 19B is a diagram illustrating equipotential lines and electriclines of force in the liquid crystal element according to Example 4.

FIG. 20A is a diagram illustrating an electric potential gradient in aliquid crystal element according to Example 5 of the present invention.FIG. 20B is a diagram illustrating equipotential lines and electriclines of force in the liquid crystal element according to Example 5.

FIG. 21A is a diagram illustrating an electric potential gradient of aconvex Fresnel lens according to Comparative Example 3. FIG. 21B is adiagram illustrating an electric potential gradient of a convex Fresnellens according to Example 6 of the present invention. FIG. 21C is adiagram illustrating an electric potential gradient of a convex Fresnellens according to Example 7 of the present invention.

FIG. 22A is a diagram illustrating an electric potential gradient of aconcave Fresnel lens according to Comparative Example 4. FIG. 22B is adiagram illustrating in an enlarged scale the electric potentialgradient of the concave Fresnel lens according to Comparative Example 4.FIG. 22C is a diagram illustrating an electric potential gradient of aconcave Fresnel lens according to Example 8 of the present invention.

FIG. 22D is a diagram illustrating in an enlarged scale the electricpotential gradient of the concave Fresnel lens according to Example 8 ofthe present invention.

FIG. 23A is a diagram illustrating an electric potential gradient of aconcave Fresnel lens according to Example 9 of the present invention.FIG. 23B is a diagram illustrating in an enlarged scale the electricpotential gradient of the concave Fresnel lens according to Example 9 ofthe present invention. FIG. 23C is a diagram illustrating an electricpotential gradient of a concave Fresnel lens according to Example 10 ofthe present invention. FIG. 23D is a diagram illustrating in an enlargedscale the electric potential gradient of the concave Fresnel lensaccording to Example 10 of the present invention.

FIG. 24 is a diagram illustrating an eyeglass device according to avariation of Embodiment 6 of the present invention.

DESCRIPTION OF EMBODIMENTS

The following describes embodiments of the present invention withreference to the drawings. In the figures of the accompanying drawings,the same reference numerals denote the same or equivalent elements inthe drawings, and the description thereof will not be repeated.Furthermore, in order to simplify the drawings, hatched lines indicatingcross-sections are omitted as appropriate. In the description of theembodiments of the present invention, refraction of light may bereferred to as deflection of the light, a refracting angle of light maybe referred to as a deflecting angle of the light, deflection of lightmay be referred to as refraction of the light, and a deflecting angle oflight may be referred to as a refracting angle of the light.

Embodiment 1

The following describes a liquid crystal element 100 according toEmbodiment 1 of the present invention with reference to FIGS. 1 to 3.The liquid crystal element 100 refracts and outputs light. In the aboveconfiguration, for example, the liquid crystal element 100 can be usedas a deflection element that deflects and outputs light or a lens thatfocuses or disperses light.

FIG. 1A is a plan view illustrating the liquid crystal element 100according to Embodiment 1. FIG. 1B is a cross-sectional view taken alongthe line IB-IB in FIG. 1A.

As illustrated in FIGS. 1A and 1B, the liquid crystal element 100includes two unit electrodes 10, an insulating layer 21, a firstboundary layer 51, a second boundary layer 52, two high-resistancelayers 22 (two resistance layers), a liquid crystal layer 23, and athird electrode 3. The unit electrodes 10 each include a first electrode1 and a second electrode 2.

The two unit electrodes 10 are disposed on the same layer level as eachother. The second electrode 2 of one unit electrode 10 of the adjacentunit electrodes 10 is adjacent to the first electrode 1 of the otherunit electrode 10.

The first electrode 1 is opposite to the third electrode 3 with theinsulating layer 21, a corresponding one of the high-resistance layers22, and the liquid crystal layer 23 therebetween. For example, the firstelectrode 1 is transparent in color and is made of indium tin oxide(ITO). The second electrode 2 is opposite to the third electrode 3 withthe insulating layer 21, a corresponding one of the high-resistancelayers 22, and the liquid crystal layer 23 therebetween. For example,the second electrode 2 is transparent in color and is made of ITO.

The first electrode 1 and the second electrode 2 constitute one unitelectrode 10 and are disposed on the same layer level. The firstelectrode 1 and the second electrode 2 of each unit electrode 10 aredisposed opposite to each other with the insulating layer 21therebetween and extend linearly with a distance W1 therebetween. Ineach unit electrode 10, the distance W1 between the first electrode 1and the second electrode 2 is larger than a width K1 of the firstelectrode and larger than a width K2 of the second electrode 2. However,the distance W1 may be set to any value. The distance W1 is a distancebetween an inner edge of the first electrode 1 and an inner edge of thesecond electrode 2. The distance W1 may be referred to also as a widthW1 of the unit electrode 10. Furthermore, a length of the firstelectrode 1 and the second electrode 2 can be set to any value.

The width K1 is a width of the first electrode 1 in a direction D1. Thewidth K2 is a width of the second electrode 2 in the direction D1. Thedirection D1 is a direction from the first electrode 1 toward the secondelectrode 2, is perpendicular to respective longitudinal directions ofthe first electrode 1 and the second electrode 2, and is substantiallyparallel to the liquid crystal layer 23.

Note that a distance W2 may be referred to also as a width W2 of theliquid crystal layer 23. The distance W2 is a distance between a firstelectrode 1 and a second electrode 2 that are disposed the most apartfrom each other. Specifically, the distance W2 is a distance between aninner edge of the first electrode 1 and an inner edge of the secondelectrode 2 that are disposed the most apart from each other.

A first voltage V1 is applied to the first electrodes 1. A secondvoltage V2 different from the first voltage V1 is applied to the secondelectrodes 2. Specifically, as illustrated in FIG. 1B, the liquidcrystal element 100 is included in a liquid crystal device 200. Theliquid crystal device 200 further includes a controller 40 such as acomputer, a first power supply circuit 41, and a second power supplycircuit 42. The controller 40 controls the first power supply circuit 41and the second power supply circuit 42.

The first power supply circuit 41 under control of the controller 40applies the first voltage V1 to the first electrodes 1. The firstvoltage V1 is alternating current voltage and has a frequency f1. Thefirst voltage V1 is for example in square waveform. The first voltage V1has a maximum amplitude V1 m. For example, the maximum amplitude V1 m isat least 0 V and no greater than 50 V and the frequency f1 is at least10 Hz and no greater than 5 MHz.

The second power supply circuit 42 under control of the controller 40applies the second voltage V2 to the second electrodes 2. The secondvoltage V2 is alternating current voltage and has a frequency f2. Thefrequency f1 and the frequency f2 are the same value as each other inEmbodiment 1. The second voltage V2 is for example in a square waveform.The second voltage V2 has a maximum amplitude V2 m. For example, themaximum amplitude V2 m is at least 2 V and no greater than 100 V.However, the maximum amplitude V2 m is larger than the maximum amplitudeV1 m in Embodiment 1. For example, the maximum amplitude V2 m is doublethe maximum amplitude V1 m. However, the maximum amplitude V2 m may besmaller than the maximum amplitude V1 m. The second voltage V2 and thefirst voltage V1 are the same as each other in phase. However, there maybe phase difference between the second voltage V2 and the first voltageV1.

Each of the frequency f1 and the frequency f2 is for example set to afavorable frequency. The favorable frequency is a frequency favorablefor formation of an electric potential gradient by which a desiredrefracting angle is attainable in the liquid crystal layer 23.

The insulating layer 21 is an electrical insulator. The insulating layer21 is disposed between each location of the first electrode 1 and thesecond electrode 2 and the high-resistance layer 22 to electricallyinsulate the first electrode 1 and the second electrode 2 from thehigh-resistance layer 22. Furthermore, in the unit electrode 10, theinsulating layer 21 is disposed between the first electrode 1 and thesecond electrode 2 to electrically insulate the first electrode 1 andthe second electrode 2 from each other. For example, the insulatinglayer 21 is transparent in color and is made of silicon dioxide (SiO₂).

The insulating layer 21 has a thickness ts. The thickness ts is athickness of a portion of the insulating layer 21 located between thefirst electrode 1 and the high-resistance layer 22 or a thickness of aportion of the insulating layer 21 located between the second electrode2 and the high-resistance layer 22.

The first boundary layer 51 is the same electric insulator as theinsulating layer 21, and is made of the same material as the insulatinglayer 21. In the above configuration, the first boundary layer 51 isformed as a part of the insulating layer 21. The first boundary layer 51is disposed between the unit electrodes 10 adjacent to each other. Thefirst boundary layer 51 is disposed between a second electrode 2 and afirst electrode 1 that are adjacent to each other. In the aboveconfiguration, the first boundary layer 51 electrically insulates thesecond electrode 2 and the first electrode 1 that are adjacent to eachother.

The two high-resistance layers 22 are provided for the respective twounit electrodes 10. The two high-resistance layers 22 are disposed onthe same layer level. Each of the high-resistance layers 22 is disposedbetween the insulating layer 21 and the third electrode 3. Specifically,each of the high-resistance layers 22 has a planar shape and is disposedbetween the insulating layer 21 and the liquid crystal layer 23 as asingle layer. Each of the high-resistance layers 22 is opposite to acorresponding one of the unit electrodes 10 with the insulating layer 21therebetween. Specifically, the first electrode 1 and the secondelectrode 2 are opposite to the high-resistance layer 22 with theinsulating layer 21 therebetween.

The high-resistance layer 22 has an electrical resistivity (specificresistance) higher than an electrical resistivity of the first electrode1, higher than an electrical resistivity of the second electrode, andlower than an electrical resistivity of the insulating layer 21. Forexample, the high-resistance layer 22 has a surface resistivity higherthan a surface resistivity of each of the first electrode 1 and asurface resistivity of the second electrode 2 and lower than a surfaceresistivity of the insulating layer 21. A surface resistivity of asubstance is a value obtained by dividing an electrical resistivity ofthe substance by a thickness of the substance.

For example, the electrical resistivity of the high-resistance layer 22is preferably at least 1 Ω·m and lower than the electrical resistivityof the insulating layer 21. It is possible for example that the surfaceresistivity of the high-resistance layer 22 is at least 5×10³ Ω/□ and nogreater than 5×10⁹Ω/□, the respective surface resistivities of the firstelectrode 1 and the second electrode 2 are at least 5×10⁻¹Ω/□ and nogreater than 5×10²Ω/□, and the surface resistivity of the insulatinglayer 21 is at least 1×10¹¹Ω/□ and no greater than 1×10¹⁵Ω/□. It ispossible for example that the surface resistivity of the high-resistancelayers 22 is at least 1×10²Ω/□ and no greater than 1×10¹¹Ω/□, therespective surface resistivities of the first electrode 1 and the secondelectrode 2 are at least 1×10⁻²Ω/□ and no greater than 1×10Ω/□, and thesurface resistivity of the insulating layer 21 is at least 1×10¹¹Ω/□ andno greater than 1×10¹⁶Ω/□. For example, the high-resistance layers 22are transparent in color and are made of zinc oxide (ZnO).

The electrical resistivity of the high-resistance layers 22 is forexample set to a favorable electrical resistivity. The favorableelectrical resistivity is an electrical resistivity favorable forformation of an electric potential gradient by which a desiredrefracting angle is attainable in the liquid crystal layer 23.

Each of the high-resistance layers 22 has a thickness th. The thicknessis of the insulating layer 21 is smaller than the thickness th of thehigh-resistance layer 22. In the above configuration, concentration ofequipotential lines substantially parallel to the direction D1 can beprevented in a part of the insulating layer 21 located between thesecond electrode 2 and the high-resistance layer 22 and a part of theinsulating layer 21 located between the first electrode 1 and thehigh-resistance layer 22. As a result, electrical potential drop andrise can be prevented in the part of the insulating layer 21 locatedbetween the second electrode 2 and the high-resistance layer 22 and thepart of the insulating layer 21 located between the first electrode 1and the high-resistance layer 22. In the following description,electrical potential drop and rise such as above may be referred to as a“potential smoothing phenomenon”.

Typically, the potential smoothing phenomenon becomes significant as thewidth W1 of the unit electrode 10 is decreased. Also, the favorablefrequency and the favorable electrical resistivity typically varyaccording to the potential smoothing phenomenon.

By contrast, occurrence of the potential smoothing phenomenon is reducedby setting the thickness ts of the insulating layer 21 smaller than thethickness th of the high-resistance layer 22 in Embodiment 1.Accordingly, occurrence of the potential smoothing phenomenon can bereduced without depending on the width W1 of the unit electrode 10. As aresult, variation of the favorable frequency and the favorableelectrical resistivity depending on the width W1 (inter-electrodedistance) of the unit electrode 10 can be prevented.

For example, the thickness ts of the insulating layer 21 is preferablyequal to or less than ⅕ of the thickness th of the high-resistance layer22 (ts≤(⅕)th). For example, the thickness ts of the insulating layer 21is preferably equal to or less than 50 nm. For example, the thickness tsof the insulating layer 21 is preferably equal to or less than 1/25 ofthe thickness th of the high-resistance layer 22 (ts≤( 1/25)th). Asmaller thickness ts of the insulating layer 21 is more preferable solong insulation is maintained between each location of the firstelectrode 1 and the second electrode 2 and the high-resistance layer 22.This is because variation of the favorable frequency and the favorableelectrical resistivity depending on the width W1 of the unit electrode10 can be prevented as the thickness ts of the insulating layer 21 isdecreased.

The second boundary layer 52 is the same electric insulator as theinsulating layer 21 and is made of the same material as the insulatinglayer 21. Therefore, the second boundary layer 52 is formed as a part ofthe insulating layer 21. However, the second boundary layer 52 may be anelectric insulator different from the insulating layer 21 and may beformed of an electric insulator of polyimide or the like that is usedfor example as an alignment material for the liquid crystal layer 23.

Furthermore, the second boundary layer 52 faces the first boundary layer51 with the insulating layer 21 therebetween. The second boundary layer52 has a width substantially the same as the first boundary layer 51.The width of the second boundary layer 52 is a width of the secondboundary layer 52 in the direction D1. The width of the first boundarylayer 51 is a width of the first boundary layer 51 in the direction D1.The second boundary layer 52 is disposed between the high-resistancelayers 22, which are adjacent to each other, to electrically insulatethe high-resistance layers 22 from each other.

The liquid crystal layer 23 includes liquid crystal. The liquid crystallayer 23 is disposed between the insulating layer 21 and the thirdelectrode 3. Specifically, the liquid crystal layer 23 is disposedbetween the high-resistance layers 22 and the third electrode 3. Forexample, the liquid crystal is nematic liquid crystal of whichorientation is homogenous in an environment with no electric filed inwhich the first voltage V1 and the second voltage V2 are not applied,and is transparent in color. The liquid crystal layer 23 has a thicknesstq. For example, the thickness tq is at least 5 μm and no greater than100 μm. The liquid crystal layer 23 includes a region A1 correspondingto one unit electrode 10 of the two unit electrodes 10 and a region A2corresponding to the other unit electrode 10.

A third voltage V3 is applied to the third electrode 3. The thirdelectrode 3 is ground and the third voltage V3 is set to a groundpotential (0 V) in Embodiment 1. The third electrode 3 has a planarshape and is formed as a single layer. For example, the third electrode3 is transparent in color and is made of ITO. For example, the firstelectrodes 1, the second electrodes 2, and the third electrode 3 havesubstantially the same electrical resistivity.

As described with reference to FIG. 1, light can be refracted whileelectric power loss can be prevented in Embodiment 1. That is, since theinsulating layer 21 insulates the first electrode and the secondelectrode 2 from each other, no electric current flows between the firstelectrode 1 and the second electrode 2. In the above configuration,electric power loss can be reduced in the liquid crystal element 100.Furthermore, when the second voltage V2 is applied to the secondelectrodes 2 while the first voltage is applied to the first electrodes1, a smooth electrical potential gradient can be formed in the liquidcrystal layer 23 in the presence of the high-resistance layers 22. As aresult, light entering the liquid crystal element 100 can be refractedat a refracting angle corresponding to the electric potential gradientwith high accuracy.

The reason why electric power loss can be prevented will be describedbelow. That is, the high-resistance layers 22 each have conductionelectrons and holes, of which amount is small though, that serve ascarries of electric current. Therefore, if the electrodes are directlyconnected to the high-resistance layers 22 for voltage application,electric current flows in a direction according to an electricalpotential difference. As a result, energy equivalent to a product of asquare of the electric current and the resistance value of thehigh-resistance layers 22 dissipates as Joule heat. The energydissipating as Joule heat corresponds to lost electric power.

By contrast, the insulating layer 21 is disposed between each locationof the first electrode 1 and the second electrode 2 and thehigh-resistance layer 22 in Embodiment 1. In the above configuration, noelectric current flows in the high-resistance layer 22. As a result,generation of Joule heat can be suppressed, and eventually, electricpower loss can be prevented.

The reason why the smooth electrical potential gradient can be formedwill be described below. That is, when the second voltage V2 is appliedto the second electrode 2 while the third voltage V3 is applied to thethird electrode 3, an electrical potential difference is producedbetween the second electrode 2 and the third electrode 3. Accordingly,electric lines of force extending from the second electrode 2 toward thethird electrode 3 are yielded based on electrical charges concentratingon the second electrode 2.

The following focuses on electric lines of force extending from an inneredge of the second electrode 2 toward the third electrode 3. If theinsulating layer 21 is provided while the high-resistance layer 22 isnot provided, the electric lines of force extend from the inner edge ofthe second electrode 2 toward the third electrode 3 across a directionD2 at substantially right angles without spreading in the direction D2.The direction D2 is a direction opposite to the direction D1. When theelectric lines of force do not spread in the direction D2 from the inneredge of the second electrode 2, a non-smooth electric potential gradientmay be formed in the liquid crystal layer 23.

By contrast, the high-resistance layer 22 dispreads, in the directionD2, the electric lines of force extending from the inner edge of thesecond electrode 2 toward the third electrode 3. As a result, theelectric lines of force spread in the direction D2. When the electriclines of force spread in the direction D2, a smooth electric potentialgradient is formed in the liquid crystal layer 23.

Further, variation of the favorable frequency and the favorableelectrical resistivity depending on the width W1 of the unit electrode10 can be prevented in Embodiment 1. Therefore, it is unnecessary todetermine the favorable frequency according to the width W1 for each ofthe liquid crystal elements 100 different from one another inspecification (width W1). Also, it is unnecessary to determine thefavorable electrical resistivity according to the width W1 for each ofthe liquid crystal elements 100 different from one another inspecification (width W1) and it is unnecessary to preparehigh-resistance layers 22 having the favorable electrical resistivityfor each of the liquid crystal elements 100 different from one anotherin specification (width W1). As a result, design complexity of theliquid crystal element 100 can be reduced and an increase inmanufacturing cost of the liquid crystal element 100 can be suppressed.

Furthermore, the widths W1 of the unit electrodes 10 are determined suchthat a ratio of refracted light to light output from the liquid crystallayer 23 (light transmitted through the liquid crystal layer 23) islarger than a ratio of diffracted light to the light output from theliquid crystal layer 23 in Embodiment 1. In the above configuration, theliquid crystal element 100 functions as a refractive lens. Further, arefractive lens can be formed while variation of the favorable frequencyand the favorable electrical resistivity depending on the width W1 ofthe unit electrode 10 can be prevented.

The following describes a mechanism by which the liquid crystal element100 refracts light with reference to FIGS. 2A, 2B, 2C, and 3. FIG. 2A isa cross-sectional view illustrating the liquid crystal element 100. FIG.2B is a diagram illustrating an electric potential gradient G2 formed inthe liquid crystal element 100. FIG. 2C is a diagram illustrating arefractive index gradient g2 formed in the liquid crystal element 100.In FIGS. 2A to 2C, points P1 to P4 each represent a position in theliquid crystal layer 23 in the direction D1. The liquid crystal layer 23includes a plurality of liquid crystal molecules 24. FIG. 3 is a diagramillustrating incident light B1 entering the liquid crystal element 100and output light B2 output from the liquid crystal element 100.

As illustrated in FIGS. 2A and 2B, when the first voltage V1 is appliedto each first electrode 1 and the second voltage V2 is applied to eachsecond electrode 2, an electric potential gradient G2 in a sawtoothshape is formed in the liquid crystal layer 23 in the presence of thehigh-resistance layers 22, the first boundary layer 51, and the secondboundary layer 52.

The electric potential gradient G2 includes two electric potentialgradients G1. That is, the respective smooth electric potentialgradients G1 extending linearly with respect to the direction D1 areformed in the region A1 and the region A2 of the liquid crystal layer 23by influence of the high-resistance layers 22. The smooth electricpotential gradients G1 mean electric potential gradients not in astepped shape. The maximum amplitude V2 m of the second voltage V2 islarger than the maximum amplitude V1 m of the first voltage V1, andtherefore, an electric potential in each electric potential gradient G1increases in the direction D1. The respective electric potentialgradients G2 continuously vary from below the first electrodes 1 tobelow the second electrodes 2 with no extremes (minimum values andmaximum values). The electric potential sharply drops in a region of theliquid crystal layer 23 that faces the second boundary layer 52. This isbecause the influence of the high-resistance layers 22 is not exerted tothe above region by providing the first boundary layer 51 and the secondboundary layer 52.

Each electric potential gradient G1 with respect to the direction D1 isrepresented by a gradient angle α1. The gradient angle α1 in the regionA1 and the gradient angle α1 in the region A2 are substantially equal toeach other.

The gradient angle α1 can be changed by changing a difference (V2 m−V1m) between the maximum amplitude V2 m of the second voltage V2 and themaximum amplitude V1 m of the first voltage V1. The shape of eachelectric potential gradient G1 is determined according to the frequencyf1, the frequency f2, and the electrical resistivity of thehigh-resistance layers 22. In Embodiment 1, the frequency f1, thefrequency f2, and the electrical resistivity of the high-resistancelayers 22 are determined such that the electric potential gradients G1each have a linear shape.

As illustrated in FIGS. 2B and 2C, the electric potential gradient G2 ina sawtooth shape is formed in the liquid crystal layer 23, with a resultthat the refractive index gradient g2 in a sawtooth shape is formed inthe liquid crystal layer 23. The refractive index gradient g2 includestwo refractive index gradients g1. That is, the respective refractiveindex gradients g1 extending linearly with respect to the direction D2are formed in the region A1 and the region A2 of the liquid crystallayer 23. The smooth index gradients g1 are formed in correspondencewith the respective smooth electric potential gradients G1. The smoothrefractive index gradients g1 means refractive index gradients not in astepped shape. In particular, optimization of the frequency f1, thefrequency f2, and the electrical resistivity of the high-resistancelayers 22 can achieve formation of further smooth electric potentialgradients G1 and further smooth refractive index gradients g1.

The refractive index of each refractive index gradient g2 increases inthe direction D2. The respective refractive index gradients g2continuously vary from below the first electrodes 1 to below the secondelectrodes 2 with no extremes (minimum values and maximum values). Arefractive index of the liquid crystal layer 23 at each of the point P1and the point P3 is represented by n1. A refractive index of the liquidcrystal layer 23 at each of the point P3 and the point P4 is representedby n2, and is smaller than n1. The refractive index n1 represents amaximum refractive index and the refractive index n2 represents aminimum refractive index in Embodiment 1.

Each refractive index gradient g1 with respect to the direction D2 isrepresented by a gradient angle β1. The gradient angle β1 is expressedby the following expression (1). The gradient angle β1 is substantiallyin proportion to the gradient angle α1. In Embodiment 1, the gradientangle β1 is substantially equal to the gradient angle α1.

β1=arctan((n1−n2)tq/W1)  (1)

As illustrated in FIGS. 2A to 2C and 3, the refractive index gradient g2in a sawtooth shape is formed in correspondence to the electricpotential gradient G2 in a sawtooth shape in the liquid crystal layer23. Accordingly, the incident light B1 entering the liquid crystal layer23 substantially perpendicularly thereto is refracted at a refractingangle γ1 corresponding to the gradient angle α1 and the gradient angleβ1 and output as the output light B2. The refracting angle γ1 is anangle of a travel direction of the output light B2 with respect to atravel direction of the incident light B1. The refracting angle γ1 issubstantially equal to the gradient angle α1 and the gradient angle β1in Embodiment 1.

Specifically, incident light B1 a of the incident light B1 enters theregion A1 and is output as output light B2 a of the output light B2.Incident light B1 b of the incident light B1 enters the region A2 and isoutput as output light B2 b of the output light B2. The gradient angleα1 in the region A1 is substantially equal to the gradient al in theregion A2, and each electric potential gradient G1 is in a smooth andlinear shape. Therefore, a wavefront of the output light B2 a and awavefront of the output light B2 b are substantially aligned in astraight line to constitute a wavefront F2. Thus, wave aberration of theoutput light B2 can be reduced.

Typically, light is refracted toward a side where the refractive indexis large. Therefore, the incident light B1 a is refracted toward a sideof the first electrode 1 of one of the unit electrodes 10 thatcorresponds to the region A1 while the incident light B1 b is refractedtoward a side of the first electrode 1 of the other unit electrode 10that corresponds to the region A2. However, it is possible to refractthe incident light B1 a toward a side of the second electrode 2 of theone unit electrode 10 that corresponds to the region A1 and refract theincident light B1 b toward a side of the second electrode 2 of the otherunit electrode 10 that corresponds to the region A2 by setting themaximum amplitude V1 m of the first voltage V1 larger than the maximumamplitude V2 m of the second voltage V2.

As described with reference to FIGS. 2A to 2C and 3, Embodiment 1provides the insulating layer 21 and the high-resistance layers 22,thereby forming the smooth electric potential gradients G1 and thesmooth refractive index gradients g1 while reducing electric power loss.As a result, the incident light B1 can be refracted according to theelectric potential gradients G1 with high accuracy.

Further, the electric potential gradient G2 is formed in the liquidcrystal layer 23 using the first electrodes 1 and the second electrodes2 disposed on the same layer level. Accordingly, the liquid crystalelement 100 with a simple configuration can be formed as compared to acase where an electric potential gradient is formed using multiple(three or more) electrodes deposed on the same layer level.

Yet, the wavefront F2 of the output light B2 is substantially in astraight line in Embodiment 1. Therefore, wave aberration of the outputlight B2 can be reduced as compared to a case where a stepped electricpotential gradient is formed using multiple (three or more) electrodesdisposed on the same layer level. Note that formation of a steppedelectric potential gradient results in a stepped wavefront of the outputlight to generate wave aberration. Furthermore, each electric potentialgradient G1 has no extremes, with a result that the wavefront F2 of theoutput light B2 can be aligned in a straighter line to allow the liquidcrystal element 100 to effectively function as a deflection element oflight.

The distance W1 between the first electrode 1 and the second electrode 2is larger than the width K1 of the first electrode 1 and larger than thewidth K2 of the second electrode 2 in Embodiment 1. In the aboveconfiguration, a ratio of a light quantity of light that is refractedand output at the refracting angle γ1 to a total light quantity of lightthat enters the liquid crystal element 100 can be easily made largerthan a ratio of a light quantity of light that travels straight andoutput to the total light quantity thereof. Therefore, the liquidcrystal element 100 can further effectively function as a deflectionelement of light. For example, it is preferable that the distance W1 isdouble or more the width K1 and double or more the width K2.

Yet, the distance W1 between the first electrode 1 and the secondelectrode 2 is set larger than the width K1 of the first electrode 1 andlarger than the width K2 of the second electrode 2 in Embodiment 1. Thehigh-resistance layer 22 spreads over a wide range from below the firstelectrode 1 to below the second electrode 2 (i.e., the distance W1 overa wide range). In the above configuration, each of the electricpotential gradients G1 having no extremes can be easily formed frombelow the first electrode 1 to below the second electrode 2 byappropriately setting the maximum amplitude V1 m, the maximum amplitudeV2 m, the frequency f1, the frequency f2, and the resistance value ofthe high-resistance layers 22. As a result, the wavefront F2 of theoutput light B2 can be aligned in a straighter line. Thus, the liquidcrystal element 100 can further effectively function as a deflectionelement of light.

Yet, the electric potential gradients G1 are formed in the liquidcrystal layer 23 in Embodiment 1 using the first electrodes 1 and thesecond electrodes 2 each of which is in a linear shape as illustrated inFIGS. 1A and 2B. Thus, respective electric potential gradient surfacesare formed in a longitudinal direction of the first electrodes 1 and thesecond electrodes 2 in the liquid crystal layer 23. Each of the electricpotential gradient surfaces is a surface formed by the electricpotential gradient G1 successive in the longitudinal direction of thefirst electrode 1 and the second electrode 2. Therefore, the incidentlight B1 can be refracted and output such that the refracting angles γ1are substantially equal in the longitudinal direction of the firstelectrodes 1 and the second electrodes 2.

(Variation)

A liquid crystal element 100 according to a variation of Embodiment 1 ofthe present invention includes one unit electrode 10. In the aboveconfiguration, the first boundary layer 51 and the second boundary layer52 are dispensed with in the present variation. The other elements ofconfiguration of the liquid crystal element 100 according to the presentvariation are all the same as those of the liquid crystal element 100according to Embodiment 1.

In the present variation, the same effects as those in Embodiment 1(where two unit electrodes 10 are provided) can be obtained. Forexample, the insulating layer 21 and a high-resistance layer 22 areprovided in the present variation, with a result that the smoothelectric potential gradients G1 can be formed while electric power losscan be reduced, thereby refracting light with high accuracy.Furthermore, for example, the thickness is of the insulating layer 21 issmaller than the thickness th of the high-resistance layer 22 in thepresent variation. Accordingly, the favorable frequency and thefavorable electrical resistivity can be prevented from varying dependenton the inter-electrode distance.

The following describes comparison in refracting angle γ1 betweenEmbodiment 1 and the present variation. The gradient angle β1 of each ofthe refractive index gradients g1 is expressed by equation (1) inEmbodiment 1 and the present variation. The gradient angle β1 inEmbodiment 1 is accordingly larger than the gradient angle β1 in thepresent variation. This is because the width W1 of each unit electrode10 in Embodiment 1 is smaller than the width W1 of the unit electrode 10of the present variation. The gradient angle β1 in Embodiment 1 beinglarger than the gradient angle β1 in the present variation means thatthe refracting angle γ1 in Embodiment 1 is larger than the refractingangle γ1 in the present variation. Therefore, in Embodiment 1, loweringin response speed of the liquid crystal molecules 24 can be prevented bysuppressing an increase in the thickness tq of the liquid crystal layer23 and the refracting angle γ1 can be made larger than the refractingangle γ1 in the present variation.

Embodiment 2

The following describes a liquid crystal element 100 according toEmbodiment 2 of the present invention with reference to FIGS. 4 to 8. InEmbodiment 2, the liquid crystal element 100 functions as a Fresnel lensthrough application of the liquid crystal element 100 according toEmbodiment 1. The liquid crystal element 100 according to Embodiment 2is the same as the liquid crystal element 100 according to Embodiment 1in that light is refracted and output. The following mainly describesdifferences of Embodiment 2 from Embodiment 1.

FIG. 4 is a plan view illustrating the liquid crystal element 100according to Embodiment 4. FIG. 5 is a plan view illustrating a part ofthe liquid crystal element 100 in an enlarged scale. FIG. 6 is across-sectional view taken along the line VI-VI in FIG. 5.

As illustrated in FIGS. 4 and 5, the liquid crystal element 100 includesa core electrode 70, a center electrode rc, unit electrodes r1 to r4,the insulating layer 21, a plurality of first boundary layers 51, afirst lead wire 71, a second lead wire 72, and a third boundary layer73. Each of the unit electrodes r1 to r4 includes the first electrode 1and the second electrode 2.

The core electrode 70 has a discoid shape and is disposed on a centerline C of the liquid crystal element 100. The discoid shape means acircular planar shape. The core electrode 70 is surrounded by the centerelectrode rc. The core electrode 70 is made of the same material as thefirst electrode 1. The core electrode 70 has a radius Ra. The radius Rais a distance from a center of gravity of the core electrode 70 to anouter edge of the core electrode 70. The center line C passes throughthe center of gravity of the core electrode 70.

The core electrode 70, the center electrode rc, the unit electrodes r1to r4, the first boundary layers 51, the first lead wire 71, the secondlead wire 72, and the third boundary layer 73 are arranged on the samelayer level.

The core electrode 70, the center electrode rc, and the unit electrodesr1 to r4 are arranged concentrically about the core electrode 70 as acenter. The core electrode 70 and the center electrode rc areelectrically insulated from each other by the insulating layer 21. Oneof the first boundary layers 51 is disposed between the center electroderc and the unit electrode r1. The respective other first boundary layers51 are disposed between the unit electrode r1 and the unit electrode r2,between the unit electrode r2 and the unit electrode r3, and between theunit electrode r3 and the unit electrode r4. Each of the first boundarylayers 51 has a ring shape a part of which is void.

Each of the center electrode rc, the first electrodes 1, and the secondelectrodes 2 has a ring shape a part of which is void. The centerelectrode rc has a radius Rc. The radius Rc is an outer radius of thecenter electrode rc. Further, the unit electrodes r1 to r4 have radii R1to R4, respectively (R4>R3>R2>R1). The radius Rc is smaller than each ofthe radii R1 to R4. The unit electrodes r1 to r4 have widths d1 to d4,respectively (d4<d3<d2<d1). Although the size of the center electrode rccan be set to any value, the radius Rc is preferably larger than each ofthe widths d1 to d4 in order to increase utilization efficiency oflight. The center electrode rc has a width Kc. The width Kc is a widthof the center electrode rc in a radial direction.

In the following description, the unit electrodes r1 to r4 may each bereferred generally to as a unit electrodes rn, a radius of the unitelectrode rn among the radii R1 to R4 may be referred to as a radius Rn,and a width of the unit electrode rn among the widths d1 to d4 may bereferred to as a width dn. A subscript n represents an integer of atleast 1 and no greater than N that is allotted to each of the unitelectrodes in ascending order from a unit electrode having the smallestradius to a unit electrode having the largest radius among the unitelectrodes. N represents the number of unit electrodes and is “4” inEmbodiment 2.

In the present specification, the subscript n may be referred to as a“unit electrode ordinal n”.

The following continues description of the liquid crystal element 100with reference to FIG. 5. As illustrated in FIG. 5, the width dn of eachof the unit electrodes rn is larger than the width K1 of the firstelectrodes 1 and larger than the width K2 of the second electrodes 2.The width dn is a distance between the first electrode 1 and the secondelectrode 2 in each of the unit electrodes rn. The width K1 is a widthof the first electrode 1 in the radial direction thereof, and the widthK2 is a width of the second electrode 2 in the radial direction thereof.

The radius Rn of a unit electrode rn is represented by a radius of thesecond electrode 2 constituting the unit electrode rn. The radius of thesecond electrode 2 is an outer radius of the second electrode 2, and theradius of the first electrode 1 is an outer radius of the firstelectrode 1. The radius of the second electrode 2 constituting a unitelectrode rn is larger than the radius of the first electrode 1constituting the unit electrode rn. The radius Rn of a unit electrode rnis expressed by the following expression (2).

[Expression 1]

Rn=(n+1)^(1/2) ×Rc  (2)

The width dn of a unit electrode rn is a distance between an outer edgeof the first electrode 1 constituting the unit electrode rn and an inneredge of the second electrode 2 constituting the unit electrode rn. Oneunit electrode rn of adjacent unit electrodes rn that has a largerradius Rn than the other unit electrode rn has a smaller width dn thanthe other unit electrode rn that has a smaller radius Rn. The unitelectrodes rn surround the center electrode rc.

The first lead wire 71 extends from the core electrode 70 toward a firstelectrode 1 having the largest radius while out of contact with thesecond electrodes 2. The first lead wire 71 has a linear shape. Thefirst lead wire 71 is made of the same material as the first electrodes1.

The core electrode 70 is connected to the first lead wire 71. One end ofopposite ends of each of the first electrodes 1 is connected to thefirst lead wire 71. In the above configuration, the first voltage V1 isapplied to the core electrode 70 and the first electrodes 1 through thefirst lead wire 71. Note that the other end 82 of the opposite ends ofeach of the first electrodes 1 is located opposite to the second leadwire 72 with the insulating layer 21 therebetween.

The radius Ra of the core electrode 70 is larger than the width Kc ofthe center electrode rc, the width K1 of the first electrodes 1, or thewidth K2 of the second electrodes 2. In Embodiment 2, the radius Ra ofthe core electrode 70 is larger than each of the width Kc of the centerelectrode rc, the width K1 of the first electrodes 1, and the width K2of the second electrodes 2. However, the radius Ra of the core electrode70 is smaller than an inner radius of the center electrode rc. That is,the radius Ra of the core electrode 70 is determined so that the coreelectrode 70 is out of contact with the center electrode rc.

The second lead wire 72 extends from the center electrode rc toward asecond electrode 2 having the largest radius among the second electrodes2 while out of contact with the first electrodes 1. The second lead wire72 has a linear shape. The second lead wire 72 is made of the samematerial as the second electrodes 2.

One end 93 of opposite ends of the center electrode rc is connected tothe second lead wire 72. One end 91 of opposite ends of each of thesecond electrodes 2 is connected to the second lead wire 72. In theabove configuration, the second voltage V2 is applied to the centerelectrode rc and the second electrodes 2 through the second lead wire72. Note that the other end 94 of the opposite ends of the centerelectrode rc is located opposite to the first lead wire 71 with theinsulating layer 21 therebetween. Also, the other end 92 of the oppositeends of each of the second electrodes 2 is located opposite to the firstlead wire 71 with the insulating layer 21 therebetween.

The third boundary layer 73 includes the same electric insulator as theinsulating layer 21 and is made of the same material as the insulatinglayer 21. Therefore, the third boundary layer 73 is formed as a part ofthe insulating layer 21. The third boundary layer 73 is disposed betweenthe first lead wire 71 and the second lead wire 72. In the aboveconfiguration, the third boundary layer 73 electrically insulates thefirst lead wire 71 and the second lead wire 72 from each other.

The following continues description of the liquid crystal element 100with reference to FIG. 6. As illustrated in FIG. 6, the liquid crystalelement 100 further includes a plurality of second boundary layers 52,the plurality of high-resistance layers 22 (resistance layers), theliquid crystal layer 23, and the third electrode 3. The thickness ts ofthe insulating layer 21 is smaller than the thickness th of thehigh-resistance layers 22. For example, the thickness ts of theinsulating layer 21 is preferably equal to or less than ⅕ of thethickness th of the high-resistance layers 22. For example, thethickness ts of the insulating layer 21 is preferably 50 nm or less. Forexample, the thickness ts of the insulating layer 21 is furtherpreferably equal to or less than 1/25 of the thickness th of thehigh-resistance layers 22. The thickness ts refers to a thickness of aportion of the insulating layer 21 located between the first electrode 1and a corresponding high-resistance layer 22, a thickness of a portionof the insulating layer 21 located between the second electrode 2 and acorresponding high-resistance layer 22, a thickness of a portion of theinsulating layer 21 located between the core electrode 70 and acorresponding high-resistance layer 22, or a thickness of a portion ofthe insulating layer 21 located between the center electrode rc and acorresponding high-resistance layer 22.

The center electrode rc and the first electrode 1 of the unit electroder1 are adjacent to each other with the first boundary layer 51therebetween. Among the unit electrodes rn, the second electrode 2 ofone of adjacent unit electrodes rn and the first electrode 1 of theother unit electrode rn are adjacent to each other with a correspondingone of the first boundary layers 51 therebetween.

The liquid crystal element 100 further includes five high-resistancelayers 22 (five resistance layers), four second boundary layers 52, theliquid crystal layer 23, and the third electrode 3. The fivehigh-resistance layers 22 and the second boundary layers 52 are disposedon the same layer level. A high-resistance layer 22 that is locatedinnermost is opposite to the core electrode 70 and the center electroderc with the insulating layer 21 therebetween, and has a discoid shape.The other four high-resistance layers 22 are opposite to the respectiveunit electrodes r1 to r4 with the insulating layer 21 therebetween, andeach have a circular band shape.

The second boundary layers 52 are each disposed between adjacenthigh-resistance layers 22. The second boundary layers 52 each have aring shape a part of which is void correspondingly to the first boundarylayer 51. Note that the first boundary layers 51 and the second boundarylayers 52 are made of the same material as the insulating layer 21 asparts of the insulating layer 21. However, the second boundary layers 52may each be an electric insulator different from the insulating layer21.

A width of the second boundary layers 52 is substantially the same as awidth of the first boundary layers 51. The width of the second boundarylayers 52 is a width of the second boundary layers 52 in a radialdirection of the second boundary layers 52. The width of the firstboundary layers 51 is a width of the first boundary layers 51 in aradial direction of the first boundary layers 51.

Note that the liquid crystal element 100 has a configuration symmetricalwith respect to the center line C of the liquid crystal element 100. Theinsulating layer 21 is disposed between each location of the coreelectrode 70 and the center electrode rc and the correspondinghigh-resistance layer 22 to insulate the core electrode 70 and thecenter electrode rc from the high-resistance layer 22. The insulatinglayer 21 is disposed between each location of the first electrodes 1 andthe second electrodes 2 and corresponding high-resistance layers 22 toelectrically insulate the first electrodes 1 and the second electrodes 2from the high-resistance layers 22. The insulating layer 21 is disposedbetween the core electrode 70 and the center electrode rc toelectrically insulate the core electrode 70 and the center electrode rcfrom each other. The insulating layer 21 is disposed between the firstelectrode 1 and the second electrode 2 of each of the unit electrodes rnto electrically insulate the first electrode 1 and the second electrode2 from each other.

Each of the high-resistance layers 22 is disposed between the insulatinglayer 21 and the third electrode 3. Specifically, each of thehigh-resistance layers 22 is disposed between the insulating layer 21and the liquid crystal layer 23. The electrical resistivity of thehigh-resistance layers 22 is higher than the electrical resistivity ofthe core electrode 70, higher than the electrical resistivity of thecenter electrode rc, higher than the electrical resistivity of the firstelectrodes 1, and higher than the electrical resistivity of the secondelectrodes 2, and smaller than the electrical resistivity of theinsulating layer 21. Furthermore, the liquid crystal layer 23 isdisposed between the insulating layer 21 and the third electrode 3.Specifically, the liquid crystal layer 23 is disposed between thehigh-resistance layers 22 and the third electrode 3. The third electrode3 has a planar shape and is opposite to the core electrode 70, thecenter electrode rc, and the unit electrodes rn with the liquid crystallayer 23, the high-resistance layers 22, and the insulating layer 21therebetween.

The following continues description of the liquid crystal element 100with reference to FIGS. 5 and 7. As illustrated in FIG. 5, the liquidcrystal element 100 further includes a counter layer 74. The counterlayer 74 extends linearly along the first lead wire 71, the thirdboundary layer 73, and the second lead wire 72. The counter layer 74 hasa width WD that is substantially equal to an interval SP1. The intervalSP1 is a distance between a straight line passing through the ends 82and a straight line passing through the ends 92. The width WD of thecounter layer 74 is a width of the counter layer 74 in a circumferentialdirection of the liquid crystal element 100.

FIG. 7 is a cross-sectional view taken along the line VII-VII in FIG. 5.As illustrated in FIG. 7, the counter layer 74 is opposite to the firstlead wire 71, the third boundary layer 73, and the second lead wire 72with the insulating layer 21 therebetween. The width WD of the counterlayer 74 is larger than an interval SP2. The interval SP2 is a distancefrom an outer edge of the first lead wire 71 to the outer edge of thesecond lead wire 72. However, the width WD of the counter layer 74 maybe equal to or larger than the interval SP2 and equal to or less thanthe interval SP1.

The counter layer 74 is the same electric insulator as the insulatinglayer 21, and is made of the same material as the insulating layer 21.Accordingly, the counter layer 74 is formed as a part of the insulatinglayer 21 in Embodiment 2. However, the counter layer 74 may be anelectric insulator different from the insulating layer 21. The counterlayer 74 and each of the high-resistance layers 22 are disposed on thesame layer level.

The following describes an electric potential gradient GF formed in theliquid crystal element 100 with reference to FIGS. 6, 8A, and 8B. FIG.8A is a plan view illustrating the liquid crystal element 100. In FIG.8A, the first lead wire 71, the second lead wire 72, and the thirdboundary layer 73 are not illustrated in order to simplify the drawing.Also, in order to simplify the drawing, the center electrode rc, thefirst electrodes 1, and the second electrodes 2 are each drawn in a ringshape with no void. FIG. 8B is a diagram illustrating the electricpotential gradient GF formed in the liquid crystal element 100. FIG. 8Billustrates the electric potential gradient GF appearing in a sectiontaken along the line A-A in FIG. 8A.

As illustrated in FIGS. 6, 8A, and 8B, when the first voltage V1 isapplied to the core electrode 70, the second voltage V2 is applied tothe center electrode rc, the first voltage V1 is applied to each of thefirst electrodes 1 of the unit electrodes r1 to r4, and the secondvoltage V2 is applied to each of the second electrodes 2 of the unitelectrodes r1 to r4, the electric potential gradient GF in a sawtoothshape that is symmetric with respect to the center line C is formed inthe liquid crystal layer 23 in the presence of the high-resistancelayers 22, the first boundary layers 51, and the second boundary layers52. In other words, the electric potential gradient Gf which isconcentric is formed when the liquid crystal element 100 is viewed inplan (that is, when the liquid crystal element 100 is viewed in adirection in which the center line C extends). Note that the firstvoltage V1 is lower than the second voltage V2 in order to form theelectric potential gradient GF illustrated in FIG. 8B.

The electric potential gradient GF includes an electric potentialgradient GFc formed correspondingly to the core electrode 70 and thecenter electrode rc, an electric potential gradient GF1 formedcorrespondingly to the unit electrode r1, an electric potential gradientGF2 formed correspondingly to the unit electrode r2, an electricpotential gradient GF3 formed correspondingly to the unit electrode r3,and an electric potential gradient GF4 formed correspondingly to theunit electrode r4. The electric potential gradient GFc and the electricpotential gradients GF1 to GF4 each are an electric potential gradientin a radial direction RD of the liquid crystal element 100. In thefollowing description, the electric potential gradient GFc may bereferred to as a “central electric potential gradient GFc”.

Due to influence of the high-resistance layers 22, each of the electricpotential gradients GF1 to GF4 is in a smooth curved shape and has nosteps and extremes (minimum values and maximum values). The electricpotential gradient GFc is also in a smooth curved shape and has no stepsin the presence of the influence of the corresponding high-resistancelayer 22. Further, the electric potential gradient GFc has no extremes(minimum values and maximum values) from the center electrode rc to thecenter line C in the presence of the influence of the high-resistancelayer 22.

The electric potential gradient GFc is for example expressed by aquadratic curve. Each of the electric potential gradient GFc and theelectric potential gradients GF1 to GF4 can be in a curved shape bysetting the frequency f1 and the frequency f2 higher than those forformation of a linear electric potential gradient. The electricpotential gradient GFc and the electric potential gradients GF1 to GF4each are formed such that the electric potential increases in the radialdirection RD of the liquid crystal element 100 from the center line C.Among the electric potential gradient GFc and the electric potentialgradients GF1 to GF4, inclination becomes steeper as an electricpotential gradient is located farther apart from the center line C.

When the electric potential gradient GF is formed in the liquid crystallayer 23, a refractive index gradient corresponding to the electricpotential gradient GF is formed in the liquid crystal layer 23. As aresult, incident light entering the liquid crystal layer 23 is refractedat respective angles corresponding to the electric potential gradientGFc and the electric potential gradients GF1 to GF4 and output from theliquid crystal layer 23 as output light. The inclination becomes steeperas an electric potential gradient is located farther apart from thecenter line C. The refracting angle accordingly increases as an electricpotential gradient is farther apart from the center line C, therebycondensing the output light toward the center line C. As a result, theliquid crystal element 100 can function as a Fresnel lens.

As described with reference to FIGS. 4 to 8B, the electric potentialgradient GF in a sawtooth shape symmetrical with respect to the centerline C can be formed in Embodiment 2, as illustrated in FIG. 8B. As aresult, the liquid crystal element 100 can function as a Fresnel lenswithout an increase in thickness of the liquid crystal layer 23.

The high-resistance layers 22 are provided for the respective unitelectrodes rn in Embodiment 2. In the above configuration, the electricpotential gradient GFc and the electric potential gradients GF1 to GF4each are smoothly curved with no steps. Thus, wave aberration of outputlight can be reduced. The electric potential gradient GFc has noextremes from the center electrode rc to the center line C. In addition,the electric potential gradient GFc and the electric potential gradientsGF1 to GF4 each have no extremes. Accordingly, incident light can beaccurately refracted, resulting in that the liquid crystal element 100can form a highly accurate Fresnel lens.

The maximum amplitude V2 m of the second voltage V2 is larger than themaximum amplitude V1 m of the first voltage V1 in Embodiment 2. In theabove configuration, a convex Fresnel lens can be formed by the liquidcrystal element 100. By contrast, it is possible to set the maximumamplitude V2 m smaller than the maximum amplitude V1 m. This can form aconcave Fresnel lens. According to Embodiment 2, both a convex Fresnellens and a concave Fresnel lens can be easily formed by the singleliquid crystal element 100 through control of the maximum amplitude V1 mand the maximum amplitude V2 m.

Furthermore, the radius Ra of the core electrode 70 is larger than thewidth Kc of the center electrode rc, larger than the width K1 of thefirst electrodes 1, and larger than the width K2 of the secondelectrodes 2 in Embodiment 2. In the above configuration, the centralelectric potential gradient GFc can be formed that is suitable for aFresnel lens. In particular, the central electric potential gradient GFccan be formed that is suitable for a concave Fresnel lens. The reasontherefor is as follows.

That is, the central electric potential gradient GFc is preferablyapproximated to an upward convex quadratic curve in a concave Fresnellens. The term “upward convex” refers to convex toward a high-resistancelayer 22 from the third electrode 3. By contrast, the term “downwardconvex” refers to convex toward the third electrode 3 from ahigh-resistance layer 22.

By contrast, in a typical situation in which electric lines of forceextend toward a third electrode from a first electrode and a secondelectrode, a central electric potential gradient tends not to beapproximate to an upward convex quadratic curve.

By contrast, in Embodiment 2, similarly to Embodiment 1, thehigh-resistance layers 22 dispread, in the direction D2, the electricline of force extending from the inner edge of the second electrode 2toward the third electrode 3. As a result, the electric lines of forcespread in the direction D2. Further, the electric lines of force morespread in the direction D2 in Embodiment 2 than those in a case wherethe radius of a core electrode is equal to or less than a width of acenter electrode, a width of first electrodes, and a width of secondelectrodes. This is because the radius Ra of the core electrode 70 islarger than the width Kc of the center electrode rc, the width K1 of thefirst electrodes 1, or the width K2 of the second electrodes 2 inEmbodiment 2. When the electric lines of force further spreads in thedirection D2, the central electric potential gradient GFc isapproximated to an upward convex quadratic curve. That is, the centralelectric potential gradient GFc can be formed that is suitable for aconcave Fresnel lens.

In particular, the radius Ra of the core electrode 70 is preferablyequal to or larger than ⅕ of the radius Rc of the center electrode rc inorder to form the central electric potential gradient GFc suitable for aconcave Fresnel lens by approximating the central electric potentialgradient GFc to an upward convex quadratic curve. Further preferably,the radius Ra of the core electrode 70 is equal to or larger than 3/10of the radius Rc of the center electrode rc. More preferably, the radiusRa of the core electrode 70 is equal to or larger than ½ of the radiusRc of the center electrode rc.

Furthermore, the thickness ts of the insulating layer 21 is smaller thanthe thickness th of the high-resistance layers 22 in Embodiment 2. Inthe above configuration, similarly to Embodiment 1, occurrence of thepotential smoothing phenomenon can be reduced without depending on thewidths dn of the unit electrodes rn. As a result, variation of thefavorable frequency and the favorable electrical resistivity dependingon the widths dn (inter-electrode distance) of the unit electrodes rncan be prevented. For example, the thickness ts of the insulating layer21 is preferably equal to or less than ⅕ of the thickness th of thehigh-resistance layers 22. For example, the thickness ts of theinsulating layer 21 is further preferably equal to or less than 1/25 ofthe thickness th of the high-resistance layers 22. A smaller thicknessts of the insulating layer 21 is more preferable so long as insulationis maintained between each location of the core electrode 70 and thecenter electrode rc and the corresponding high-resistance layer 22,between each location of the first electrodes 1 and the secondelectrodes 2 and the corresponding high-resistance layers 22. This isbecause variation of the favorable frequency and the favorableelectrical resistivity depending on the widths dn of the unit electrodesrn can be reduced more as the thickness ts of the insulating layer 21 isdecrease.

In particular, the width dn of a unit electrode rn located more outwardin the radial direction of the liquid crystal element 100 is smaller inEmbodiment 2. However, variation of the favorable frequency and thefavorable electrical resistivity depending on the width dn of the unitelectrode rn can be prevented in Embodiment 2. Accordingly, it isunnecessary to make both the frequency f1 of the first voltage V1 andthe frequency f2 of the second voltage V2 different between a unitelectrode rn located inward in the radial direction of the liquidcrystal element 100 and a unit electrode rn located outward in theradial direction thereof and it is unnecessary to additionally make theelectrical resistivities of the high-resistance layers 22 differentbetween a unit electrode rn located inward in the radial direction ofthe liquid crystal element 100 and a unit electrode rn located outwardin the radial direction thereof. As a result, design complexity of theliquid crystal element 100 can be reduced and an increase inmanufacturing cost of the liquid crystal element 100 can be suppressed.

Furthermore, the widths dn of the unit electrodes rn are determined suchthat a ratio of refracted light to light output from the liquid crystallayer 23 (light transmitted through the liquid crystal layer 23) islarger than a ratio of diffracted light to the light output from theliquid crystal layer 23 in Embodiment 2. In the above configuration, theliquid crystal element 100 functions as a refractive lens. Further, arefractive lens can be formed while variation of the favorable frequencyand the favorable electrical resistivity depending on the widths dn ofthe unit electrodes rn can be reduced.

Similarly to Embodiment 1, each width dn (distance between a firstelectrode 1 and a second electrode 2) is larger than the width K1 of thefirst electrode 1 and larger than the width K2 of the second electrode 2in Embodiment 2. In the above configuration, a ratio of a light quantityof light, which is refracted and output, to a total light quantity oflight entering the liquid crystal element 100 can be easily made largerthan a ratio of a light quantity of light, which travels straight and isoutput, to the total light quantity thereof. The width dn is for exampledouble or more the width K1 of the first electrode 1 and double or moreof the width K2 of the second electrode 2.

Further, similarly to Embodiment 1, the width dn is larger than thewidth K1 of the first electrode 1 and larger than the width K2 of thesecond electrode 2 in Embodiment 2. Further, each high-resistance layer22 is disposed over a wide range from below a corresponding firstelectrode 1 to below a corresponding second electrode 2 (i.e., the widthdo in a wide range). In the above configuration, the respective electricpotential gradients G1 to GF4 having no extremes can be easily formedfrom below the first electrodes 1 to below the second electrodes 2 byappropriately setting the maximum amplitude V1 m, the maximum amplitudeV2 m, the frequency f1, the frequency f2, and the resistance value ofthe high-resistance layers 22.

Furthermore, when the center electrode rc and the unit electrodes rn areformed so that expression (2) is satisfied, a Fresnel lens having alarge refracting angle can be formed efficiently only through control ofthe two voltages of the first voltage V1 and the second voltage V2 inEmbodiment 2.

Yet, similarly to Embodiment 1, only control of the maximum amplitude V1m of the first voltage V1 or the maximum amplitude V2 m of the secondvoltage V2 can facilitate change of the respective gradient angles ofthe electric potential gradient GFc and the electric potential gradientsGF1 to GF4 and eventually the refracting angle while keeping thethickness of the liquid crystal layer 23. In other words, only controlof the maximum amplitude V1 m of the first voltage V1 or the maximumamplitude V2 m of the second voltage V2 can change the focal length ofthe Fresnel lens over between the positive polarity and the negativepolarity. Thus, focus control over a wide operation range can beachieved in the single liquid crystal element 100.

Furthermore, similarly to Embodiment 1, the electric potential gradientGF and the refractive index gradient can be formed with electric powerloss reduced and light can be refracted in Embodiment 2.

Still, the liquid crystal element 100 according to Embodiment 2 includesthe counter layer 74. The counter layer 74 is an electric isolator. Inthe above configuration, interference can be prevented between anelectric potential derived from the first voltage V1 at and in thevicinity of the end 82 of each first electrode 1 and an electricpotential derived from the second voltage V2 from the second lead wire72 as compared to a case where a high-resistance layer 22 is disposed ata location where the counter layer 74 is disposed in place of thecounter layer 74. Furthermore, interference can be reduced between anelectric potential derived from the second voltage V2 at and in thevicinity of the end 92 of each second electrode 2 and an electricpotential derived from the first voltage V1 from the first lead wire 71.As a result, the electric potential gradients GF with less strain can beformed concentrically when the liquid crystal element 100 is viewed inplan, resulting in formation of a further accurate Fresnel lens.

In addition, since the first lead wire 71 and the second lead wire 72are provided in Embodiment 2, it is possible to reduce in manufacturingcost as compared to a case where through holes for the first electrodes1 and through holes for the second electrodes 2 are formed.

Note that the liquid crystal element 100 is included in the liquidcrystal device 200 (see FIG. 1B) similarly to Embodiment 1. Therefore,the first power supply circuit 41 applies the first voltage V1 to thefirst lead wire 71. Also, the second power supply circuit 42 applies thesecond voltage V2 to the second lead wire 72.

(Variation 1)

In Variation 1 of Embodiment 2 of the present invention, the radius Raof the core electrode 70 is less than ⅕ of the radius Rc of the centerelectrode rc. Further, the radius Ra of the core electrode 70 may beequal to or less than the width Kc of the center electrode rc, equal toor less than the width K1 of the first electrode 1, and equal to or lessthan the width K2 of the second electrode 2 in Variation 1. In Variation1, the thickness is of the insulating layer 21 is smaller than thethickness th of the high-resistance layers 22. In the aboveconfiguration, variation of the favorable frequency and the favorableelectrical resistivity depending on the widths do of the unit electrodesrn can be reduced similarly to Embodiment 2.

(Variation 2)

In Variation 2 of Embodiment 2 of the present invention, the thicknessis of the insulating layer 21 is equal to or larger than the thicknessth of the high-resistance layers 22. In Variation 2, the radius Ra ofthe core electrode 70 is larger than the width Kc of the centerelectrode rc, the width K1 of the first electrode 1, or the width K2 ofthe second electrode 2. In the above configuration, the central electricpotential gradient GFc can be formed that is suitable for a concaveFresnel lens.

Embodiment 3

The following describes a liquid crystal element 100 according toEmbodiment 3 of the present invention with reference to FIGS. 5, 6, and9. The liquid crystal element 100 according to Embodiment 3 differs fromthe liquid crystal element 100 according to Embodiment 2 illustrated inFIG. 6 in non-inclusion of the insulating layer 21 illustrated in FIG.6. However, respective insulating layers 21 is located between the coreelectrode 70 and the center electrode rc and between the first electrode1 and the second electrode 2. The following mainly describes differencesof Embodiment 3 from Embodiment 2.

FIG. 9 is a cross-sectional view illustrating the liquid crystal element100 according to Embodiment 3. As illustrated in FIG. 9, the liquidcrystal element 100 includes the core electrode 70, the center electroderc, the unit electrodes r1 to r4, a plurality of insulating layers 21, aplurality of first boundary layers 51, a plurality of second boundarylayers 52, the plurality of high-resistance layers 22 (resistancelayers), the liquid crystal layer 23, and the third electrode 3.

As illustrated in FIG. 9, the liquid crystal layer 23 is disposedbetween each unit electrode rn and the third electrode and between eachlocation of the core electrode 70 and the center electrode rc and thethird electrode 3. Specifically, the liquid crystal layer 23 is disposedbetween the high-resistance layers 22 and the third electrode 3.

The high-resistance layers 22 each are disposed between a correspondingone of the unit electrodes rn and the liquid crystal layer 23 andbetween each location of the core electrode 70 and the center electroderc and the liquid crystal layer 23. The unit electrodes rn are eachopposite to a corresponding one of the high-resistance layers 22 with noinsulator therebetween while in contact with the high-resistance layer22. Each of the core electrode 70 and the center electrode rc isopposite to the corresponding the high-resistance layer 22 with noinsulator therebetween while in contact with the high-resistance layer22. The electrical resistivity of the high-resistance layers 22 is lowerthan the electrical resistivity of the insulator.

The widths dn of the unit electrodes rn are determined as follows. Thatis, the widths dn of the unit electrodes are determined so that a ratioof refracted light to light output from the liquid crystal layer 23(light transmitted through the liquid crystal layer 23) is larger than aratio of diffracted light to the light output therefrom. In the aboveconfiguration, the liquid crystal element 100 functions as a refractivelens rather than a diffractive lens. In other words, the widths dn ofthe unit electrodes are determined so that light entering the liquidcrystal layer 23 is bent more largely as the wavelength of the lightbecomes shorter. The refractive lens deflects or condenses light bybending the light through refraction. Note that the widths of the unitelectrodes for a diffractive lens are determined so that light enteringthe liquid crystal layer is bent more largely as the wavelength of thelight becomes longer. The diffractive lens condenses light by bendingthe light through diffraction.

The following describes difference between the liquid crystal element100 functioning as a Fresnel lens that is a refractive lens and a liquidcrystal element functioning as a diffractive lens of blazed type withreference to FIG. 10. In the liquid crystal element functioning as ablazed type diffractive lens, a core electrode, a center electrode, anda plurality of unit electrodes are arranged concentrically about thecore electrode as a center. An electric potential gradient having ablazed cross section is formed in a liquid crystal layer. The electricpotential gradient having a blazed cross section is an electricpotential gradient having a sawtooth shape in cross section.

FIG. 10 is a graph representation showing a relationship between theunit electrode ordinal n and radius Rn of the unit electrodes rn of theliquid crystal elements 100 each functioning as a Fresnel lens and arelationship between the unit electrode ordinal n and radius Rn of unitelectrodes rn of the liquid crystal elements each functioning as ablazed type diffractive lens. Definitions of the unit electrode ordinaln and the radius Rn of each unit electrode of the liquid crystalelements each functioning as a blazed type diffractive lens are the sameas those of the unit electrode ordinal n and the radius Rn of each unitelectrode rn of the liquid crystal element 100 described with referenceto FIG. 5, respectively.

As shown in FIG. 10, a curved line 85 represents the relationshipbetween the unit electrode ordinal n and the radius Rn of the unitelectrodes rn of the liquid crystal element 100 functioning as a Fresnellens having a focal length of 10 mm. By contrast, a curved line 87represents the relationship between the unit electrode ordinal n and theradius Rn of the unit electrodes of the liquid crystal elementfunctioning as a blazed type diffractive lens having a focal length of10 mm. A curved line 86 represents the relationship between the unitelectrode ordinal n and the radius Rn of the unit electrodes of theliquid crystal element 100 functioning as a Fresnel lens having a focallength of 20 mm. By contrast, a curved line 88 represents therelationship between the unit electrode ordinal n and the radius Rn ofthe unit electrodes of the liquid crystal element functioning as ablazed type diffractive lens having a focal length of 20 mm. Note thatthe wavelength of a light source is 568 nm in calculation of the unitelectrode ordinal n of the unit electrodes of the liquid crystalelements each functioning as a blazed type diffractive lens.

The curved lines 85 to 88 show that when the unit electrode ordinal n ofthe unit electrodes is the same among the Fresnel lenses and the blazedtype diffractive lenses, the radii Rn of the respective unit electrodesrn of the Fresnel lenses are larger than the radii Rn of the respectiveunit electrodes rn of the blazed type diffractive lenses. Accordingly,in light contributing to imaging in each Fresnel lens, a ratio ofrefracted light to light output from the liquid crystal layer 23 islarger than a ratio of diffracted light to the light output from theliquid crystal layer 23. By contrast, a ratio of the diffracted light tothe light output from the liquid crystal layer 23 is larger than a ratioof the refracted light thereto in the light contributing to imaging ineach blazed type diffractive lens.

As described with reference to FIGS. 9 and 10, the liquid crystalelement 100 according to Embodiment 3 functions as a Fresnel lens thatis a refractive lens. Therefore, the focal length can be set to anyvalue by controlling the widths dn of the unit electrodes rn, thefrequency f1 and the maximum amplitude V1 m of the first voltage V1, andthe frequency f2 and the maximum amplitude V2 m of the second voltageV2. That is, the focal length can be easily set to any value since thenumber of controllable parameters is large. Note that the focal lengthcan be changed only by changing the widths dn of the unit electrodes rnin a blazed type diffractive lens. That is, it is difficult to set thefocal length to any value since the number of controllable focalparameter is small.

Furthermore, it is preferable to allow white light to enter the liquidcrystal element 100 in Embodiment 3 in order that the liquid crystalelement 100 further effectively functions as a Fresnel lens that is arefractive lens. This is because influence of diffraction can be reducedto a minimum with use of the white light, which includes wavelengthcomponents over a wide range and has small coherency. Note that a blazedtype diffractive lens uses diffracted light, and therefore, incidence ofmonochromatic light having high coherency, such as laser light ispreferable.

Furthermore, the unit electrodes rn each are opposite to a correspondingone of the high-resistance layers 22 with no insulator therebetweenwhile in contact with the high-resistance layer 22 in Embodiment 3. Eachof the core electrode 70 and the center electrode rc is opposite to thecorresponding high-resistance layer 22 with no insulator therebetweenwhile in contact with the high-resistance layers 22. In the aboveconfiguration, Joule heat may be generated in the high-resistance layers22.

Therefore, a refractive lens that can effectively utilize the Joule heatcan be formed in Embodiment 3. That is, the liquid crystal layer 23 iswarmed by being heated by the Joule heat from the high-resistance layers22. Thus, reduction in response speed of the liquid crystal molecules 24can be prevented. In particular, favorable response speed of the liquidcrystal molecules 24 can be maintained even when the temperature of anenvironment where the liquid crystal element 100 is set is low (forexample, even in a sub-zero environment) as well as when the temperatureof the environment is comparatively high.

Moreover, the same effects as those in the liquid crystal element 100according to Embodiment 2 can be obtained in the liquid crystal element100 according to Embodiment 3. For example, variation of the favorablefrequency and the favorable electrical resistivity depending on thewidths do (inter-electrode distance) of the unit electrodes rn can bereduced. This is because the thickness is of the insulating layer 21(see FIG. 6) is equivalent to “0” in Embodiment 3. For example, arefractive lens can be formed while variation of the favorable frequencyand the favorable electrical resistivity depending on the width do(inter-electrode distance) of the unit electrode rn can be prevented.For example, an electric potential gradient suitable for a Fresnel lenscan be formed. Furthermore, the same variation as Variation 1 ofEmbodiment 2 is applicable to the liquid crystal element 100 accordingto Embodiment 3.

Embodiment 4

The following describes a liquid crystal element 100 according toEmbodiment 4 of the present invention with reference to FIGS. 9 and 11.Embodiment 4 differs from Embodiment 3 illustrated in FIG. 9 inlocations of the high-resistance layers 22. The following mainlydescribes difference of Embodiment 4 from Embodiment 3.

FIG. 11 is a cross-sectional view illustrating the liquid crystalelement 100 according to Embodiment 4. As illustrated in FIG. 11, theliquid crystal layer 23 is disposed between each unit electrode rn andthe third electrode, between each location of the core electrode 70 andthe center electrode rc and the third electrode 3.

The high-resistance layers 22 are each disposed on the opposite side ofa corresponding one of the unit electrodes rn to the liquid crystallayer 23 and on the opposite side of the core electrode 70 and thecenter electrode rc to the liquid crystal layer 23.

The unit electrodes rn are each disposed between a corresponding one ofthe high-resistance layers 22 and the liquid crystal layer 23, and thecore electrode 70 and the center electrode rc are disposed between acorresponding one of the high-resistance layer 22 and the liquid crystallayer 23. Each of the unit electrodes rn is opposite to thecorresponding high-resistance layer 22 without no insulator therebetweenwhile in contact with the high-resistance layer 22. Each of the coreelectrode 70 and the center electrode rc is opposite to thecorresponding high-resistance layer 22 with no insulator therebetweenwhile in contact with the high-resistance layer 22. In the aboveconfiguration, Joule heat can be generated in each high-resistance layer22.

The widths dn of the unit electrodes rn are determined in a mannersimilar to that in Embodiment 3. In the above configuration, the liquidcrystal element 100 functions as a Fresnel lens that is a refractivelens.

Moreover, the same effects as those in the liquid crystal element 100according to Embodiment 3 can be obtained in the liquid crystal element100 according to Embodiment 4. For example, a refractive lens that caneffectively utilize the Joule heat can be formed. For example, variationof the favorable frequency and the favorable electrical resistivitydepending on the widths dn of the unit electrodes rn (inter-electrodedistance) can be reduced. This is because the thickness is of theinsulating layer 21 (see FIG. 6) is equivalent to “0” in Embodiment 4.Furthermore, the same variation as Variation 1 of Embodiment 2 isapplicable to the liquid crystal element 100 according to Embodiment 4.

Embodiment 5

The following describes a deflection element 250 according to Embodiment5 of the present invention with reference to FIGS. 1 and 12. Thedeflection element 250 according to Embodiment 5 uses two liquid crystalelements 100 each according to Embodiment 1 described with reference toFIG. 1 for light deflection. The following mainly describes a differenceof Embodiment 5 from Embodiment 1.

FIG. 12 is a partially exploded perspective view illustrating thedeflection element 250 according to Embodiment 5. As illustrated in FIG.12, the deflection element 250 includes a first substrate 33, a liquidcrystal element 100A, a second substrate 34, a liquid crystal element100B, and a third substrate 35. The configuration of each of the liquidcrystal element 100A and the liquid crystal element 100B are the same asthe configuration of the liquid crystal element 100 according toEmbodiment 1.

The liquid crystal element 100A is disposed between the first substrate33 and the second substrate 34. The liquid crystal element 100B isdisposed between the second substrate 34 and the third substrate 35. Thefirst to third substrates 33 to 35 each are transparent in color, andeach are made of glass.

Each of the first electrodes 1 and the second electrodes 2 of the liquidcrystal element 100A extends in a first direction FD. The firstdirection FD is substantially perpendicular to a direction DA in theliquid crystal element 100A. The same definition as for the direction D1in Embodiment 1 is applied to the direction DA. Each of the firstelectrodes 1 and the second electrodes 2 of the liquid crystal element100B extends in a second direction SD perpendicular to the firstdirection FD. The second direction SD is substantially perpendicular toa direction DB in the liquid crystal element 100B. The same definitionas for the direction D1 in Embodiment 1 is applied to the direction DB.The liquid crystal element 100A and the liquid crystal element 100B areoverlaid one on the other with the second substrate 34 therebetween.

Furthermore, respective first power supply circuits 41 as illustrated inFIG. 1A are prepared for the liquid crystal element 100A and the liquidcrystal element 100B. In the above configuration, one of the first powersupply circuits 41 applies the first voltage V1 to the first electrodes1 of the liquid crystal element 100A while the other of the first powersupply circuits 41 applies the first voltage V1 to the first electrodes1 of the liquid crystal element 100B. Respective second power supplycircuits 42 are prepared for the liquid crystal element 100A and theliquid crystal element 100B. In the above configuration, one of thesecond power supply circuits 42 applies the second voltage V2 to thesecond electrodes 2 of the liquid crystal element 100A while the otherof the second power supply circuits 42 applies the second voltage V2 tothe second electrodes 2 of the liquid crystal element 100B.

The controller 40 individually controls the first power supply circuit41 and the second power supply circuit 42 for the liquid crystal element100A and the first power supply circuit 41 and the second power supplycircuit 42 for the liquid crystal element 100B. In the aboveconfiguration, the electric potential gradient G2 and the refractiveindex gradient g2 are formed individually in each of the liquid crystalelement 100A and the liquid crystal element 100B.

Incident light entering the deflection element 250 is deflected in adirection according to the electric potential gradient G2 and therefractive index gradient g2 determined by the first voltage V1 and thesecond voltage V2 each applied to the liquid crystal element 100A andthe electric potential gradient G2 and the refractive index gradient g2determined by the first voltage V1 and the second voltage V2 eachapplied to the liquid crystal element 100B. The incident light is thenoutput as output light. That is, the incident light can be deflected inany direction by controlling either or both the first voltage V1 and thesecond voltage V2 applied to the liquid crystal element 100A and eitheror both the first voltage V1 and the second voltage V2 applied to theliquid crystal element 100B.

As described with reference to FIG. 12, the unit electrodes 10 of theliquid crystal element 100A are disposed substantially perpendicular tothe unit electrodes 10 of the liquid crystal element 100B in Embodiment5. In the above configuration, incident light can be deflected in a widerange as compared to the liquid crystal element 100 according toEmbodiment 1.

Embodiment 6

The following describes an eyeglass device 280 according to Embodiment 6of the present invention with reference to FIGS. 4 and 13. The eyeglassdevice 280 according to Embodiment 6 uses as lenses of eyeglasses 300two liquid crystal elements 100 each according to Embodiment 2 describedwith reference to FIG. 4. That is, the liquid crystal elements 100refract and output light as lenses of the eyeglasses 300.

FIG. 13 is a diagram illustrating the eyeglass device 280 according toEmbodiment 6. As illustrated in FIG. 13, the eyeglass device 280includes the eyeglasses 300 and an operation device 350.

The eyeglasses 300 include a pair of control sections 65, a pair of theliquid crystal elements 100, a pair of rims 301, a pair of temples 303(pair of temple members), and a bridge 305. The control sections 65 eachinclude the controller 40, the first power supply circuit 41, and thesecond power supply circuit 42. Each of the controllers 40 includes acommunication device 64.

The rims 301 hold the respective liquid crystal elements 100 that eachare a lens. The bridge 305 joins the paired rims 301. The temples 303each are connected to an end of a corresponding one of the rims 301. Thetemples 303 each are for example an elongate member traversing from theend of the corresponding rim 301 to an ear of a user by way of a user'stemple.

Each of the liquid crystal elements 100 is the liquid crystal element100 according to Embodiment 2. The controller 40, the first power supplycircuit 41, and the second power supply circuit 42 are the same as thecontroller 40, the first power supply circuit 41, and the second powersupply circuit 42 illustrated in FIG. 1B, respectively. One of thepaired control sections 65 controls one of the paired liquid crystalelements 100, while the other of the paired control sections 65 controlsthe other of the paired liquid crystal elements 100. The communicationdevice 64 communicates with the operation device 350.

The operation device 350 is operated by a user of the eyeglasses 300.The operation device 350 includes an operation section 351 and acontroller 353. The controller 353 includes a communication device 353a. The operation section 351 receives user operation and outputs to thecontroller 353 operation signals according to the operation. Theoperation section 351 for example includes a touch panel and/or a keyset. The controller 353 causes the communication device 535 a totransmit to the eyeglasses 300 control signals according to theoperation signals.

The control signals each are a signal for setting in a liquid crystalelement 100 the frequency f1 and the maximum amplitude V1 m of the firstvoltage V1 applied to the liquid crystal elements 100 and the frequencyf2 and the maximum amplitude V2 m of the second voltage V2 applied tothe liquid crystal element 100. A control signal for controlling one ofthe liquid crystal elements 100 is transmitted to a corresponding one ofthe communication devices 64, while a control signal for controlling theother liquid crystal element 100 is transmitted to the othercommunication device 64.

The controllers 40 of the eyeglasses 300 receive the control signalsfrom the operation device 350 via the respective communication devices64. The controllers 40 control the first power supply circuits 41 andthe second power supply circuits 42 according to the control signals toset the frequencies f1 and the maximum amplitudes V1 m of the firstvoltages V1 and the frequencies f2 and the maximum amplitudes V2 m ofthe second voltages V2 for the respective liquid crystal elements 100.That is, the controllers 40 control the first voltages V1 applied to thefirst electrodes 1 and the second voltages V2 applied to the secondelectrodes 2 according to the control signals.

The focal lengths of the liquid crystal elements 100 are set based onthe first voltages V1 and the second voltages V2. In the aboveconfiguration, the user of the eyeglasses 300 can easily change thediopter of the eyeglasses 300 by operating the operation device 350.Further, the user of the eyeglasses 300 can adjust the eyeglasses 300 tobe nearsighted glasses or farsighted glasses by operating the operationdevice 350.

Note that the communication devices 64 and the communication device 353a each are for example a short-range wireless communication device. Theshort-range wireless communication device for example executesshort-range wireless communication in accordance with Bluetooth(registered Japanese trademark).

The following specifically describes the present invention usingexamples. However, the present invention is not limited to the followingexamples.

EXAMPLES

The following describes Examples 1 to 10 of the present invention andComparative Examples 1 to 4 with reference to FIGS. 14 to 23C. Thefollowing description uses the same reference signs among Examples 1 to10 and Comparative Examples 1 to 4 for the sake of description. Further,a horizontal axis indicates radius Rn (μm) of a unit electrode rn and avertical axis indicates voltage (V) in each of FIGS. 14 to 23C, unlessotherwise stated. That is, the horizontal axis indicates a position in aliquid crystal element 100 in the radial direction on the assumptionthat the position of the center line C of the liquid crystal element 100is represented by “0”.

In Examples 1 to 10 according to the present invention and ComparativeExamples 1 to 4, the frequency f1 of the first voltage V1, the frequencyf2 of the second voltage V2, and the electrical resistivity Rh of thehigh-resistance layers 22 were set to the favorable frequency and thefavorable electrical resistivity according to the unit electrodes rneach having a radius Rn in a range from 0 μm to 2,000 μm. The maximumamplitude V1 m of the first voltage V1 was 1 V and the maximum amplitudeV2 m of the second voltage V2 was 2 V in formation of a convex Fresnellens. The maximum amplitude V1 m of the first voltage V1 was 2 V and themaximum amplitude V2 m of the second voltage V2 was 1 V in formation ofa concave Fresnel lens. The electrical resistivity Rh of thehigh-resistance layers 22 was 1×10³ Ω·m. An electric potential gradientformed in each liquid crystal layer 23 was calculated.

The liquid crystal element 100 according to Embodiment 2 described withreference to FIGS. 4 to 8B was used as each of the liquid crystalelements according to Examples 1, 2, and 4 to 10. The liquid crystalelement 100 according to Embodiment 3 described with reference to FIGS.9 and 10 was used as the liquid crystal element according to Example 3.Note that the insulating layer 21 in the liquid crystal element 100according to Embodiment 3 is not disposed between each location of thecore electrode 70 and the center electrode rc and the high-resistancelayers 22 and between the unit electrodes rn and the high-resistancelayers 22. Accordingly, the thickness is of the insulating layer 21 is“0” in the liquid crystal element 100 according to Embodiment 3.

Examples 1 to 3

The following describes the liquid crystal elements 100 according toExamples 1 to 3 of the present invention and the liquid crystal elementaccording to Comparative Example 1 with reference to FIGS. 14 to 17.

In each of Examples 1 to 3 and Comparative Example 1, an electricpotential gradient was calculated through simulation under the followingconditions. The thickness of the insulating layer of the liquid crystalelement according to Comparative Example 1 differed from the thicknessts of the insulating layer 21 according to Examples 1 and 2. The liquidcrystal elements according to Examples 1 and 2 and Comparative Example 1had the same configuration as one another other than the above aspect.In each of Examples 1 and 2 and Comparative Example 1, the frequency f1of the first voltage V1 and the frequency f2 of the second voltage V2each were 200 Hz. In Example 3, the frequency f1 of the first voltage V1and the frequency f2 of the second voltage V2 each were 20 Hz. Thethickness th of the high-resistance layers 22 was 250 nm. The number ofthe unit electrodes rn was “225”. However, electric potential gradientscorresponding to 20 unit electrodes rn of the 225 unit electrodes rnwere shown in FIGS. 14 to 17.

In Comparative Example 1, the thickness ts of the insulating layer 21was 500 nm. Accordingly, ts equaled 2th.

In Example 1, the thickness ts of the insulating layer 21 was 50 nm.Accordingly, ts equaled (⅕)th.

In Example 2, the thickness ts of the insulating layer 21 was 10 nm.Accordingly, ts equaled ( 1/25)th.

In Example 3, the thickness ts of the insulating layer 21 was 0 nm.

FIG. 14 is a diagram illustrating electric potential gradients in theliquid crystal element according to Comparative Example 1. Asillustrated in FIG. 14, when the thickness ts of the insulating layer 21was larger than the thickness th of the high-resistance layers 22, anelectric potential gradient corresponding to the unit electrodes rn eachhaving a radius Rn of equal to or larger than 9,700 μm, that is, anelectric potential gradient corresponding to unit electrodes rn eachhaving a comparatively small width dn was not in a sawtooth shape, andwas leveled. That is, the electric potential was attenuated and aportion of the electric potential gradient that was to be inclined wasnot inclined and was in an almost horizontal shape. Thus, it could beconfirmed that the frequency f1 and the frequency f2 each were not thefavorable frequency and the electrical resistivity Rh was not thefavorable electrical resistivity for the unit electrodes rn each havinga comparatively small width dn. In other words, it could be confirmedthat the favorable frequency and the favorable electrical resistivitydepended on the widths dn of the unit electrodes rn.

FIG. 15 is a diagram illustrating electric potential gradients in theliquid crystal element 100 according to Example 1. FIG. 16 is a diagramillustrating electric potential gradients in the liquid crystal element100 according to Example 2. As illustrated in FIGS. 15 and 16, when thethickness is of the insulating layer 21 was smaller than the thicknessth of the high-resistance layers 22, an electric potential gradient in asawtooth shape was formed in the liquid crystal layer 23 over the unitelectrodes rn. It could be accordingly confirmed that the frequency f1and the frequency f2 each were the favorable frequency and theelectrical resistivity Rh was the favorable electrical resistivity inall of the unit electrodes rn. In other words, variation of thefavorable frequency and the favorable electrical resistivity dependingon the widths dn of the unit electrodes rn could be prevented.

Examples 1 and 2 were compared in electric potential gradientcorresponding to the unit electrodes rn each having a radius Rn of equalto or larger than 9,700 μm. As illustrated in FIGS. 15 and 16, theelectric potential gradient in the liquid crystal element 100 accordingto Example 2 had larger steps (difference between maximum electricpotential and minimum electric potential) and a larger inclination thanthat in the liquid crystal element 100 according to Example 1.Consequently, variation of the favorable frequency and the favorableelectrical resistivity depending on the widths dn of the unit electrodesrn could be prevented more as the thickness ts of the insulating layer21 is decreased.

FIG. 17 is a diagram illustrating electric potential gradients in theliquid crystal element 100 according to Example 3. As illustrated inFIG. 17, when the thickness ts of the insulating layer 21 was “0”, anelectric potential gradient in a sawtooth shape was formed over theentire unit electrodes rn. Consequently, it could be confirmed that thefrequency f1 and the frequency f2 each were the favorable frequency andthe electrical resistivity Rh was the favorable electrical resistivityin all of the unit electrodes rn. In other words, variation of thefavorable frequency and the favorable electrical resistivity dependingon the widths dn of the unit electrodes rn could be prevented.

Examples 4 and 5

The following describes the liquid crystal elements 100 according toExamples 4 and 5 of the present invention and the liquid crystal elementaccording to Comparative Example 2 with reference to FIGS. 18A to 20B.

In each of Examples 4 and 5 and Comparative Example 2, an electricpotential gradient was calculated through simulation under the followingconditions. The thickness of the insulating layer of the liquid crystalelement according to Comparative Example 2 differed from the thicknessts of each insulating layer 21 according to Examples 4 and 5. The liquidcrystal elements according to Examples 4 and 5 and Comparative Example 2had the same configuration as one another other than the above aspect.In each of Examples 4 and 5 and Comparative Example 2, the frequency f1of the first voltage V1 and the frequency f2 of the second voltage V2each were 100 Hz. The thickness th of the high-resistance layers 22 was250 nm. The number of the unit electrodes rn was “225”. However, anelectric potential gradient corresponding to 6 unit electrode rn of the225 unit electrodes rn was sown in each of FIGS. 18A to 20B.

In Comparative Example 2, the thickness ts of the insulating layer 21was 500 nm. Accordingly, ts equaled to 2th.

In Example 4, the thickness ts of the insulating layer 21 was 50 nm.Accordingly, ts equaled (⅕)th.

In Example 5, the thickness ts of the insulating layer 21 was 20 nm.Accordingly, ts equaled ( 2/25)th.

FIGS. 18A to 20B illustrate the unit electrodes rn each having a size ofaround 14,800 μm, that is, the electrode units rn each having acomparatively small width dn.

FIG. 18A is a diagram illustrating an electric potential gradient in theliquid crystal element according to Comparative Example 2. Asillustrated in FIG. 18A, when the thickness ts of the insulating layer21 was larger than the thickness th of the high-resistance layers 22(ts=2th), an electric potential gradient corresponding to the unitelectrodes rn each having a comparatively small width dn was not in asawtooth shape and was flattened.

FIG. 18B is a diagram illustrating electric lines of force EF andequipotential lines EL in the liquid crystal element according toComparative Example 2. As illustrated in FIG. 18B, multiple electriclines of force EF extending from the unit electrodes rn toward the thirdelectrode 3 were formed.

Equipotential lines EL substantially parallel to the direction D1concentrated on parts of the insulating layer 21 located between thefirst electrodes 1 and the high-resistance layers 22. Equipotentiallines EL substantially parallel to the direction D1 concentrated onparts of the insulating layer 21 located between the second electrodes 2and the high-resistance layers 22. Therefore, the potential smoothingphenomenon occurred in the insulating layer 21, with a result that anelectric potential gradient was not in a sawtooth shape and wasflattened as illustrated in FIG. 18A. In Comparative Example 2, thepotential smoothing phenomenon in the insulating layer 21 was moresignificant as the widths dn of the unit electrodes rn is decreased.

FIG. 19A is a diagram illustrating an electric potential gradient in theliquid crystal element 100 according to Example 4. As illustrated inFIG. 19A, when the thickness ts of the insulating layer 21 was smallerthan the thickness th of the high-resistance layers 22 (ts=(⅕)th), evenan electric potential gradient corresponding to the unit electrodes rneach having a comparatively small width dn was in a sawtooth shape.

FIG. 19B is a diagram illustrating electric lines of force EF andequipotential lines EL in the liquid crystal element 100 according toExample 4. As illustrated in FIG. 19B, multiple electric lines of forceEF extending from the unit electrodes rn toward the third electrode 3were formed.

Although not seen in FIG. 19B, concentration of equipotential lines ELsubstantially parallel to the direction D1 was reduced in parts of theinsulating layer 21 located between the first electrodes 1 and thehigh-resistance layers 22. Concentration of equipotential lines ELsubstantially parallel to the direction D1 was also reduced in parts ofthe insulating layer 21 located between the second electrodes 2 and thehigh-resistance layers 22. Therefore, the potential smoothing phenomenonwas reduced in the insulating layer 21, with a result that even anelectric potential gradient corresponding to the unit electrodes rn eachhaving a comparatively small width dn was in a favorable sawtooth shapeas illustrated in FIG. 19A.

FIG. 20A is a diagram illustrating an electric potential gradient in theliquid crystal element 100 according to Example 5. As illustrated inFIG. 20A, when the thickness ts of the insulating layer 21 was smallerthan the thickness th of the high-resistance layers 22 (ts=( 2/25)th),even an electric potential gradient corresponding to the unit electrodesrn each having a comparatively small width dn was in a sawtooth shape.

FIG. 20B is a diagram illustrating electric lines of force EF andequipotential lines EL in the liquid crystal element 100 according toExample 5. As illustrated in FIG. 20B, multiple electric lines of forceEF extending from the unit electrodes rn toward the third electrode 3were formed.

Although not seen in FIG. 20B, concentration of equipotential lines ELsubstantially parallel to the direction D1 was reduced more than inExample 4 in parts of the insulating layer 21 located between the firstelectrodes 1 and the high-resistance layers 22. Concentration ofequipotential lines EL substantially parallel to the direction D1 wasalso reduced more than in Example 4 in parts of the insulating layer 21located between the second electrodes 2 and the high-resistance layers22. As a result, the potential smoothing phenomenon hardly occurred inthe insulating layer 21, and even an electric potential gradientcorresponding to the unit electrodes rn each having a comparativelysmall width dn was in a further favorable sawtooth shape as illustratedin FIG. 20A.

Comparison between Examples 4 and 5 could confirm that the potentialsmoothing phenomenon could be reduced more in the insulating layer 21 asthe thickness of the insulating layer 21 was decreased. In other words,variation of the favorable frequency and the favorable electricalresistivity depending on the widths dn of the unit electrodes rn couldbe reduced more as the thickness ts of the insulating layer 21 wasdecreased.

Examples 6 and 7

The following describes liquid crystal elements according to Example 6and 7 of the present invention and a liquid crystal element according toComparative Example 3 with reference to FIG. 21.

In each of Examples 6 and 7 and Comparative Example 3, a convex Fresnellens was formed and an electric potential gradient was calculatedthrough simulation under the following conditions. The radius of thecore electrode of the liquid crystal element according to ComparativeExample 3 differed from the radius Ra of the core electrode 70 of eachof Examples 6 and 7. The liquid crystal elements according to Examples 6and 7 and the comparative example had the same configuration as oneanother other than the above aspect. In each of Examples 6 and 7 andComparative Example 3, the frequency f1 of the first voltage V1 and thefrequency f2 of the second voltage V2 each were 200 Hz. The number ofthe unit electrodes rn was “3”.

In Comparative Example 3, the radius Ra of the core electrode 70 was 50μm. The radius Ra of the core electrode 70 was substantially equal tothe width Kc of the center electrode rc. In other words, the radius Raof the core electrode 70 was 1/20 of the radius Rc of the centerelectrode rc (Ra=( 1/20)Rc).

In Example 6, the radius Ra of the core electrode 70 was 200 μm. Theradius Ra of the core electrode 70 was larger than the width Kc of thecenter electrode rc. In other words, the radius Ra of the core electrode70 was ⅕ of the radius Rc of the center electrode rc (Ra=(⅕)Rc).

In Example 7, the radius Ra of the core electrode 70 was 300 μm. Theradius Ra of the core electrode 70 was larger than the width Kc of thecenter electrode rc. In other words, the radius Ra of the core electrode70 was 3/10 of the radius Rc of the center electrode rc (Ra=( 3/10)Rc).

FIG. 21A is a diagram illustrating an electric potential gradient in theliquid crystal element according to Comparative Example 3. FIG. 21B is adiagram illustrating an electric potential gradient in the liquidcrystal element 100 according to Example 6. FIG. 21C is a diagramillustrating an electric potential gradient in the liquid crystalelement 100 according to Example 7. Note that an electric potentialgradient corresponding to the unit electrodes rn each having a radius Rnlarger than 2,000 μm was omitted.

In each of Comparative Example 3 and Examples 6 and 7, a centralelectric potential gradient GFc corresponding to the core electrode 70and the center electrode rc was approximate to a downward convexquadratic curve. That is, the central electric potential gradient GFcwas favorable for forming a convex Fresnel lens. This was because waveaberration brought about by a Fresnel lens in imaging could be reducedmore as the central electric potential gradient GFc was more approximateto a downward convex quadratic curve.

Examples 8 to 10

The following describes liquid crystal elements 100 according toExamples 8 to 10 of the present invention and a liquid crystal elementaccording to Comparative Example 4 with reference to FIGS. 22A to 23D.

In each of Examples 8 to 10 and the comparative example, a concaveFresnel lens was formed and an electric potential gradient wascalculated through simulation under the following conditions. The radiusof the core electrode of the liquid crystal element according toComparative Example 4 differed from the radius Ra of the core electrode70 of each of Examples 8 to 10. The liquid crystal elements according toExamples 8 to 10 and Comparative Example 4 had the same configuration asone another other than the above aspect. In each of Examples 8 to 10 andComparative Example 4, the frequency f1 of the first voltage V1 and thefrequency f2 of the second voltage V2 each were 200 Hz. The number ofthe unit electrodes rn was “3”.

In Comparative Example 4, the radius Ra of the core electrode 70 was 50μm. The radius Ra of the core electrode 70 was substantially equal tothe width Kc of the center electrode rc. In other words, the radius Raof the core electrode 70 was 1/20 of the radius Rc of the centerelectrode rc (Ra=( 1/20)Rc).

In Example 8, the radius Ra of the core electrode 70 was 200 μm. Theradius Ra of the core electrode 70 was larger than the width Kc of thecenter electrode rc. In other words, the radius Ra of the core electrode70 was ⅕ of the radius Rc of the center electrode rc (Ra=(⅕)Rc).

In Example 9, the radius Ra of the core electrode 70 was 300 μm. Theradius Ra of the core electrode 70 was larger than the width Kc of thecenter electrode rc. In other words, the radius Ra of the core electrode70 was 3/10 of the radius Rc of the center electrode rc (Ra=( 3/10)Rc).

In Example 10, the radius Ra of the core electrode 70 was 500 μm. Theradius Ra of the core electrode 70 was larger than the width Kc of thecenter electrode rc. In other words, the radius Ra of the core electrode70 was ½ of the radius Rc of the center electrode rc (Ra=(½)Rc).

FIG. 22A is a diagram illustrating an electric potential gradient in theliquid crystal element according to Comparative Example 4. FIG. 22B is adiagram illustrating a central electric potential gradient GFc in theliquid crystal element according to Comparative Example 4. Asillustrated in FIGS. 22A and 22B, the central electric potentialgradient GFc was approximate to a downward convex quadratic curve QC1,was not approximate to an upward convex quadratic curve, and therefore,was not favorable for a concave Fresnel lens. The quadratic curve QC1was calculated though approximation of the central electric potentialgradient GFc by the least-square method.

FIG. 22C is a diagram illustrating an electric potential gradient in theliquid crystal element 100 according to Example 8. FIG. 22D is a diagramillustrating a central electric potential gradient GFc in the liquidcrystal element 100 according to Example 8. As illustrated in FIGS. 22Cand 22D, the central electric potential gradient GFc was approximate toan upward convex quadratic curve QC2 and was favorable for a concaveFresnel lens. The central electric potential gradient GFc was madeapproximate to the upward convex quadratic curve QC2 by setting theradius Ra of the core electrode 70 to ⅕ of the radius Rc of the centerelectrode rc. The quadratic curve QC2 was calculated thoughapproximation of the central electric potential gradient GFc by theleast-square method. The value of a determination coefficient (squarevalue of a correlation coefficient) was “0.9051”, which was close to anideal value “1”.

FIG. 23A is a diagram illustrating an electric potential gradient in theliquid crystal element 100 according to Example 9. FIG. 23B is a diagramillustrating a central electric potential gradient GFc in the liquidcrystal element 100 according to Example 9. As illustrated in FIGS. 23Aand 23B, the central electric potential gradient GFc was approximate tothe upward convex quadratic curve QC2 and was favorable for a concaveFresnel lens. The central electric potential gradient GFc was furtherapproximate to the upward convex quadratic curve QC2 by setting theradius Ra of the core electrode 70 to 3/10 of the radius Rc of thecenter electrode rc. The quadratic curve QC2 was calculated thoughapproximation of the central electric potential gradient GFc by theleast-square method. The value of a determination coefficient (squarevalue of a correlation coefficient) was “0.9423”, which was furtherclose to the ideal value “1”. Therefore, a configuration in which theradius Ra was 3/10 of the radius Rc was more favorable for a concaveFresnel lens than a configuration in which the radius Ra was ⅕ of theradius Rc.

FIG. 23C is a diagram illustrating an electric potential gradient in theliquid crystal element 100 according to Example 10. FIG. 23D is adiagram illustrating a central electric potential gradient GFc in theliquid crystal element 100 according to Example 10. As illustrated inFIGS. 23C and 23D, the central electric potential gradient GFc wasapproximate to the upward convex quadratic curve QC2 and was favorablefor a concave Fresnel lens. The central electric potential gradient GFcwas further approximate to the upward convex quadratic curve QC2 bysetting the radius Ra of the core electrode 70 to ½ of the radius Rc ofthe center electrode rc. The quadratic curve QC2 was calculated thoughapproximation of the central electric potential gradient GFc by theleast-square method. The value of a determination coefficient (squarevalue of a correlation coefficient) was “0.9659”, which was furtherclose to the ideal value “1”. Therefore, a configuration in which theradius Ra was ½ of the radius Rc was more favorable for a concaveFresnel lens than a configuration in which the radius Ra was 3/10 of theradius Rc.

As illustrated in FIGS. 23A to 23D, in a configuration in which theradius Ra of the core electrode 70 was equal to or larger than 3/10 ofthe radius Rc of the center electrode rc, the central electric potentialgradient GFc was approximate to the upward convex quadratic curve QC2even when an apex of the quadratic curve QC2 was set to a levelequivalent to the maximum amplitude V1 m of the first voltage V1 appliedto the core electrode 70. Note that an electric potential gradientcorresponding to the unit electrodes rn each having a radius Rn largerthan 2,000 μm was omitted in FIGS. 22A to 23D.

Embodiments and Examples of the present invention have been described sofar with reference to the drawings (FIGS. 1A to 23D). However, thepresent invention is not limited to Embodiments and Examples asdescribed above, and may be implemented in various different forms thatdo not deviate from the essence of the present invention (for example,as described below in sections (1) to (6)). The drawings schematicallyillustrate elements of configuration in order to facilitateunderstanding and properties of elements of configuration illustrated inthe drawings, such as thickness, length, and number may differ fromactual properties thereof in order to facilitate preparation of thedrawings. Furthermore, properties of elements of configuration describedin the above embodiments, such as shapes and dimensions, are merelyexamples and are not intended as specific limitations. Variousalterations may be made so long as there is no substantial deviationfrom the effects of the present invention. In the following description,Embodiment 1 includes the variation and Embodiment 2 includes Variations1 and 2, unless otherwise explicitly stated.

(1) In each of Embodiments 1 to 6, three or more unit electrodes 10 orthree or more unit electrodes rn can be provided. In a configurationwith a plurality of the unit electrodes 10 or rn, the maximum amplitudeV1 m, the frequency f1, the maximum amplitude V2 m, and the frequency f2can be controlled for each unit electrode 10 or rn. The number of theunit electrodes rn may be one. The second boundary layer(s) 52 may eachbe a resistor having an electrical resistivity higher than theelectrical resistivity of the high-resistance layers 22. The counterlayer 74 may also be a resistor having an electrical resistivity higherthan the electrical resistivity of the high-resistance layers 22. Themaximum amplitude V1 m and the maximum amplitude V2 m are controlled,while effective values of the first voltage V1 and the second voltage V2can also be controlled.

A boundary electrode(s) may be provided in place of each of the firstboundary layer(s) 51. In the above configuration, the high-resistancelayers 22 are disposed without providing the second boundary layer(s)52. A boundary voltage different from the first and second voltages V1and V2 is applied to the boundary electrode. The boundary voltage islower than one of the first and second voltages V1 and V2 that is higherthan the other. The frequency of the boundary voltage is higher than thefrequency f1 of the first voltage V1 and the frequency f2 of the secondvoltage V2. The boundary electrode is electrically insulated from thefirst electrode 1 and the second electrode 2 by an insulating film. Forexample, the boundary electrode is transparent in color. Even in aconfiguration with the boundary electrode, an electric potentialgradient G2 and a refractive index gradient g2 similarly to those inEmbodiment 1 can be formed in the liquid crystal layer 23. The boundaryelectrode has an electrical resistivity for example substantially equalto the electrical resistivity of the first electrode(s) 1.

One unit electrode 10 of two unit electrodes 10 included in the unitelectrodes 10 may have a width W1 different from the width of the otherunit electrode 10. One unit electrode dn of two unit electrodes dnincluded in the unit electrodes dn may have a width dn different fromthe width of the other unit electrode dn. Even in the above examples,variation of the favorable frequency and the favorable electricalresistivity depending on the widths W1 of the unit electrodes 10 or thewidths dn of the unit electrodes rn can be reduced. Therefore, it isunnecessary to differentiate the frequency f1 of the first voltage V1and the frequency f2 of the second voltage V2 for each of the unitelectrodes 10 or the unit electrodes rn and it is additionallyunnecessary to differentiate the electrical resistivity of thehigh-resistance layers 22 for each of the unit electrodes 10 or the unitelectrodes rn. As a result, design complexity of the liquid crystalelement 100 can be reduced and an increase in manufacturing cost of theliquid crystal element 100 can be suppressed.

In each unit electrode 10, a gas (e.g., air) may be filled between thefirst electrode 1 and the second electrode 2 as an insulating layerrather than the insulating layer 21. Similarly, a gas may be filled asan insulating layer rather than the insulating layer 21 between the coreelectrode 70 and the center electrode rc, between the center electroderc and the first electrode 1, and between the first electrode and thesecond electrode 2 of each unit electrode rn. In addition, a gas may befilled as the first boundary layer(s) 51. Note that the insulating layer21 may not be provided between the unit electrodes 10 and thehigh-resistance layers 22.

In each of Embodiments 1 to 6, the first voltage V1 is applied to thefirst electrode 1 and the core electrode 70 and the second voltage V2 isapplied to the second electrode 2 and the center electrode rc. Themaximum amplitude V1 m of the first voltage V1 and the maximum amplitudeV2 m of the second voltage V2 differ from each other, and the frequencyf1 of the first voltage V1 and the frequency f2 of the second voltage V2are equal to each other. Note that the frequency f1 and the frequency f2may differ from each other.

However, it is possible that a core voltage is applied to the coreelectrode 70 rather than the first voltage V1 and a center voltage isapplied to the center electrode rc rather than the second voltage V2. Amaximum amplitude of the core voltage differs from a maximum amplitudeof the center voltage. A frequency of the core voltage is equal to afrequency of the center voltage. Note that the frequency of the corevoltage may differ from the frequency of the center voltage. Thefrequency of the core voltage differs from the frequency f1 of the firstvoltage V1 and the frequency f2 of the second voltage V2. The frequencyof the center voltage differs from the frequency f1 of the first voltageV1 and the frequency f2 of the second voltage V2.

The central electric potential gradient GFc can be further approximateto a quadratic curve by differentiating the frequency of the corevoltage and the frequency of the center voltage from the frequency f1and the frequency f2 and controlling the frequency of the core voltageand the frequency of the center voltage separately from the frequency f1of the first voltage V1 and the frequency f2 of the second voltage V2.As a result, a further accurate Fresnel lens can be formed.

Note that in a situation in which a convex Fresnel lens is formed, forexample, the maximum amplitude of the center voltage is larger than themaximum amplitude of the core voltage and the maximum amplitude V2 m ofthe second voltage V2 is larger than the maximum amplitude V1 m of thefirst voltage V1. In a situation in which a concave Fresnel lens isformed, for example, the maximum amplitude of the center voltage issmaller than the maximum amplitude of the core voltage and the maximumamplitude V2 m of the second voltage V2 is smaller than the maximumamplitude V1 m of the first voltage V1.

(2) In each of Embodiments 2 (except Variation 2) to 4 and 6, the coreelectrode 70 can be dispensed with. In such a case, the center electroderc and the unit electrodes rn are arranged concentrically about thecenter electrode rc as a center. Furthermore, the first lead wires 71,the second lead wires 72, the third boundary layer 73, and the counterlayer 74 may be dispensed with. In such a case, a plurality of throughholes are formed for application of the first voltage V1 and the secondvoltage V2. In a case where the through holes are formed, each of thecenter electrode rc, the first electrodes 1, and the second electrodes 2has a ring shape with no voids. In Embodiment 5, the liquid crystalelement 100 in any of Embodiments 2 to 4 can be used. In Embodiment 6,the liquid crystal element 100 in any of Embodiments 1, 3, and 4 can beused.

(3) In each of Embodiments 5 and 6, for example, the liquid crystallayer 23 may be formed of a liquid crystal material (liquid crystalmolecules 24) having no polarization dependency or a liquid crystalmaterial having polarization dependency. In a case where the liquidcrystal material has polarization dependency, for example, two liquidcrystal elements 100A and 100B having the same configuration as eachother are preferably arranged such that an angle is substantially 90degrees between the alignment direction of the liquid crystal materialof one liquid crystal element 100A of the liquid crystal elements 100Aand 100B and the alignment direction of the other liquid crystal element100B.

(4) In Embodiment 6, use of the liquid crystal element 100 is notlimited to use as a lens. The liquid crystal element 100 may be usableas an element utilizing refraction of light other than the lens.

(5) The following describes an eyeglass device 280 according to avariation of Embodiment 6 of the present invention with reference toFIG. 24. The variation differs from Embodiment 6 in that eyeglasses(also referred to below as an “eyeglasses 300A”) of the eyeglass device280 according to the variation functions as a head mounted display.

FIG. 24 is a diagram illustrating the eyeglass device 280 according tothe variation. As illustrated in FIG. 24, the eyeglass device 280according to the variation includes the eyeglasses 300A. The eyeglasses300A further includes an image output section 75 and a display 76 inaddition to the elements of configuration of the eyeglasses 300according to Embodiment 6 described with reference to FIG. 13. Elementsof configuration of the eyeglass device 280 according to the variationother than the above are all the same as those in the eyeglass device280 according to Embodiment 6.

The image output section 75 receives image data from the controller 40or the operation device 350. The image output section 75 outputs lightrays representing an image based on the image data to the display 76.The image output section 75 for example includes a projector.

The display 76 is mounted on one of the liquid crystal elements 100. Thedisplay 76 is clear and transparent. The term “transparent” herein maymean colorless and transparent or colored and transparent. However, whenthe light rays output by the image output section 75 and representingthe image enter the display 76, the display 76 displays the imagerepresented by the light rays. As a result, the user can recognize theimage. The display 76 includes for example a sheet-shaped holographicoptical element.

As described with reference to FIG. 24, the eyeglasses 300A according tothe variation can display an image. That is, the eyeglasses 300Afunctions as a head mounted display. In addition, the eyeglasses 300Aincludes the liquid crystal elements 100 each as a lens. In the aboveconfiguration, either or both an object and a background come intouser's eyes and the image on the display 76 also comes into user's eyesthrough the liquid crystal elements 100. As a result, for example, theeyeglasses 300A are suitable as a tool for realizing augmented reality(AR).

Furthermore, according to the variation, a focal length of theeyeglasses 300A, which include the same liquid crystal elements 100 asin Embodiment 6, can be freely adjusted. Therefore, the eyeglasses 300Acan display an image while achieving focus control suitable forproperties of the user's eyes. As a result, for example, the eyeglasses300A are further suitable as a tool for realizing augmented reality(AR).

Furthermore, the eyeglasses 300A are also suitable as a tool forrealizing virtual reality (VR). Note that although only one image outputsection 75 and only one display 76 are provided, paired output sections75 and paired displays 76 may be provided.

(6) In the present specification and claims, the linear shape includessubstantially linear shapes in addition to strictly linear shapes. Thecircular shape includes substantially circular shapes in addition tostrictly circular shapes. The ring shape includes ring shapes a part ofeach of which is void in addition to ring shapes with no voids. Theconcentric arrangement and formation include substantially concentricarrangement and formation in addition to strictly concentric arrangementand formation. The planar shape includes substantially planar shapes inaddition to strictly planar shapes. The sawtooth shape includessubstantially sawtooth shapes in addition to strictly sawtooth shapes.The annular shape includes substantially annular shapes in addition to astrictly annular shape. The band shape includes substantially bandshapes in addition to strictly band shapes. The curved shape includessubstantially curved shapes in addition to strictly curved shapes.

INDUSTRIAL APPLICABILITY

The present invention provides a liquid crystal element, a deflectionelement, and eyeglasses, and has industrial applicability.

REFERENCE SINGS LIST

-   -   1 First electrode    -   2 Second electrode    -   3 Third electrode    -   10 Unit electrode    -   21 Insulating layer    -   22 High-resistance layer (resistance layer)    -   23 Liquid crystal layer    -   40 Controller    -   70 Core electrode    -   100 Liquid crystal element    -   100A Liquid crystal element    -   100B Liquid crystal element    -   250 Deflection element    -   300 Eyeglasses    -   300A Eyeglasses    -   303 Temple (temple member)    -   rc Center electrode    -   r1 to r4 (rn) Unit electrode

1. A liquid crystal element that refracts and outputs light, comprising:a first electrode; a second electrode; an insulating layer that is anelectric insulator; a resistance layer; a liquid crystal layer includingliquid crystal; and a third electrode, wherein the insulating layer isdisposed between each location of the first electrode and the secondelectrode and the resistance layer, the insulating layer insulating thefirst electrode and the second electrode from the resistance layer, theresistance layer has an electrical resistivity that is higher than anelectrical resistivity of the first electrode and lower than anelectrical resistivity of the insulating layer, the resistance layer andthe liquid crystal layer are disposed between the insulating layer andthe third electrode, the resistance layer is disposed between theinsulating layer and the liquid crystal layer, and the insulating layerhas a thickness that is smaller than a thickness of the resistancelayer.
 2. The liquid crystal element according to claim 1, wherein thethickness of the insulating layer is equal to or less than ⅕ of thethickness of the resistance layer.
 3. The liquid crystal elementaccording to claim 1, wherein the first electrode and the secondelectrode constitute a unit electrode, the unit electrode is provided asa plurality of unit electrodes, one unit electrode of at least two unitelectrodes included in the unit electrodes has a width different from awidth of the other of the at least two unit electrodes, and widths ofthe unit electrodes each indicate a distance between the first electrodeand the second electrode.
 4. A liquid crystal element that refracts andoutputs light, comprising: a plurality of unit electrodes each includinga first electrode and a second electrode; a resistance layer; a liquidcrystal layer including liquid crystal; and a third electrode, whereinthe resistance layer has an electrical resistivity that is higher thanan electrical resistivity of the first electrode and lower than anelectrical resistivity of an insulator, the liquid crystal layer isdisposed between the unit electrodes and the third electrode, theresistance layer is disposed between the liquid crystal layer and theunit electrodes, or the unit electrodes are disposed between theresistance layer and the liquid crystal layer, the unit electrodes areopposite to the resistance layer with no insulator therebetween, widthsof the unit electrodes are determined such that a ratio of refractedlight to light output from the liquid crystal layer is larger than aratio of diffracted light to the light output from the liquid crystallayer, and the widths of the unit electrodes each indicate a distancebetween the first electrode and the second electrode.
 5. The liquidcrystal element according to claim 4, further comprising a centerelectrode having a ring shape, wherein the center electrode and the unitelectrodes are arranged concentrically about the center electrode as acenter.
 6. A liquid crystal element that refracts and outputs light,comprising: a core electrode; a center electrode surrounding the coreelectrode; a unit electrode including a first electrode and a secondelectrode and surrounding the center electrode; an insulating layer thatis an electric insulator; a resistance layer; a liquid crystal layerincluding liquid crystal; and a third electrode, wherein the insulatinglayer is disposed between each location of the core electrode and thecenter electrode and the resistance layer to insulate the core electrodeand the center electrode from the resistance layer, and is disposedbetween each location of the first electrode and the second electrodeand the resistance layer to insulate the first electrode and the secondelectrode from the resistance layer, the resistance layer has anelectrical resistivity that is higher than an electrical resistivity ofthe core electrode and lower than an electrical resistivity of theinsulating layer, the resistance layer and the liquid crystal layer aredisposed between the insulating layer and the third electrode, theresistance layer is disposed between the insulating layer and the liquidcrystal layer, and a distance from a center of gravity of the coreelectrode to an outer edge of the core electrode is larger than a widthof the center electrode, a width of the first electrode, or a width ofthe second electrode.
 7. The liquid crystal element according to claim6, wherein the core electrode has a discoid shape, the center electrodehas a ring shape, and the core electrode has a radius that is equal toor larger than ⅕ of a radius of the center electrode.
 8. The liquidcrystal element according to claim 6, wherein a first voltage is appliedto the first electrode, a second voltage is applied to the secondelectrode, a core voltage is applied to the core electrode, a centervoltage is applied to the center electrode, a frequency of the corevoltage differs from a frequency of the first voltage and a frequency ofthe second voltage, and a frequency of the center voltage differs fromthe frequency of the first voltage and the frequency of the secondvoltage.
 9. The liquid crystal element according to claim 1, wherein thefirst electrode and the second electrode constitute a unit electrode,and in the unit electrode, a distance between the first electrode andthe second electrode is larger than a width of the first electrode andlarger than a width of the second electrode.
 10. A deflection elementthat deflects and outputs light, comprising: two liquid crystal elementseach according to claim 1, wherein in one liquid crystal element of thetwo liquid crystal elements, the first electrode and the secondelectrode each extend in a first direction, in the other liquid crystalelement of the two liquid crystal elements, the first electrode and thesecond electrode each extend in a second direction perpendicular to thefirst direction, and the one liquid crystal element and the other liquidcrystal element are overlaid one on the other.
 11. Eyeglassescomprising: the liquid crystal element according to claim 1; acontroller configured to control a first voltage applied to the firstelectrode and a second voltage applied to the second electrode; and apair of temple members, wherein the liquid crystal element refracts andoutputs the light.
 12. The liquid crystal element according to claim 4,wherein in the unit electrode, a distance between the first electrodeand the second electrode is larger than a width of the first electrodeand larger than a width of the second electrode.
 13. The liquid crystalelement according to claim 6, wherein in the unit electrode, a distancebetween the first electrode and the second electrode is larger than awidth of the first electrode and larger than a width of the secondelectrode.
 14. A deflection element that deflects and outputs light,comprising: two liquid crystal elements each according to claim 4,wherein in one liquid crystal element of the two liquid crystalelements, the first electrode and the second electrode each extend in afirst direction, in the other liquid crystal element of the two liquidcrystal elements, the first electrode and the second electrode eachextend in a second direction perpendicular to the first direction, andthe one liquid crystal element and the other liquid crystal element areoverlaid one on the other.
 15. A deflection element that deflects andoutputs light, comprising: two liquid crystal elements each according toclaim 6, wherein in one liquid crystal element of the two liquid crystalelements, the first electrode and the second electrode each extend in afirst direction, in the other liquid crystal element of the two liquidcrystal elements, the first electrode and the second electrode eachextend in a second direction perpendicular to the first direction, andthe one liquid crystal element and the other liquid crystal element areoverlaid one on the other.
 16. Eyeglasses comprising: the liquid crystalelement according to claim 4; a controller configured to control a firstvoltage applied to the first electrode and a second voltage applied tothe second electrode; and a pair of temple members, wherein the liquidcrystal element refracts and outputs the light.
 17. Eyeglassescomprising: the liquid crystal element according to claim 6; acontroller configured to control a first voltage applied to the firstelectrode and a second voltage applied to the second electrode; and apair of temple members, wherein the liquid crystal element refracts andoutputs the light.